Variable-power optical system and electronic device using same

ABSTRACT

The invention relates to a zoom optical system that makes it possible to offer a sensible tradeoff between cost savings and size reductions and an electronic system that incorporates it. The zoom optical system comprises a lens group having negative refracting power and a lens group having positive refracting power. At least one lens is formed by molding of a first lens blank ( 11 ) that provides a surface including at least an optical function surface after molding, and a second lens blank ( 12 ) that provides a surface other than said surface including at least an optical function surface after molding, wherein the first lens blank ( 11 ) and the second lens blank ( 12 ) are integrated into a one-piece lens ( 10 ).

This is a 371 national phase application of PCT/JP2004/017028 filed 10Nov. 2004, claiming priority to Japanese Patent Applications No.2003-386162 and No. 2003-386163, both filed 17 Nov. 2003, No.2003-389222 and No. 2003-389223, both filed 19 Nov. 2003, No.2003-393936, No. 2003-393937 and No. 2003-393938, all filed 25 Nov.2003, the contents of which are incorporated herein by reference.

TECHNICAL ART

The present invention relates generally to a zoom optical system and anelectronic system incorporating it, and more particularly to a compactzoom optical system and an electronic system incorporating it. Thiselectronic system, for instance, includes digital cameras, videocameras, digital video units, personal computers, mobile computers,cellular phones and personal digital assistants.

BACKGROUND ART

Recently, personal digital assistants acronymed as PDAs and cellularphones have undergone explosive growth in demand. Some such systems havedigital camera or digital video functions added to them. To implementthese functions, CCD (charge coupled device) or CMOS (complementarymetal oxide semiconductor) sensors are now used as image pickup devices.To reduce the sizes of such systems, it is preferable to use an imagepickup device having a relatively small light receiving area. In thiscase, a sensible tradeoff between size reductions and cost savings mustbe made while the performance of an optical system is kept high. Sizereductions are now achieved by reducing the number of lenses used. Onthe other hand, cost reductions by use of a fewer step, for instance, isnow achieved by use of a fabrication process wherein lenses are formedunder pressure in a lens holder.

For reductions in the number of lenses that form an optical system, itis necessary to use aspheric lenses. For the fabrication of suchaspheric lenses, use is generally made of a fabrication process whereina preform is pressed in a state softened by heating (hereinafter calledthe prior art lens processing). With this prior art lens processing, anaspheric lens is formed larger than the required outer diameter, androunding is carried out in such a way as to incorporate it in a lensbarrel. For this reason, for instance, the thickness of the outerperiphery of the lens at the necessary outer diameter will become largerthan that of the lens during rounding. A reduction in the number oflenses for compactness will result in an increase in lens thickness,because the refracting power of each of lenses inclusive of a positivelens will become strong. For this reason and to give the lens asufficient peripheral thickness, the peripheral thickness of the lens atthe necessary outer diameter will become far larger. Thus, no sufficienteffect on size reductions will still be obtained.

On the other hand, Patent Publication 1 says nothing about not only sizereductions but also conditions for size reductions.

Patent Publication 1

JP(A)61-114822

SUMMARY OF THE INVENTION

Such being the prior art situations, the primary object of the inventionis to provide a zoom optical system that can offer an effective tradeoffbetween cost reductions and size reductions, and an electronic systemincorporating it.

According to the first aspect of the invention, there is provided a zoomoptical system comprising a lens group having negative refracting powerand a lens group having positive refracting power, characterized in thatat least one lens is formed by molding of a first lens blank thatprovides a surface including at least an optical function surface aftermolding, and a second lens blank that provides a surface other than saidsurface including at least an optical function surface after molding,wherein the first lens blank and the second lens blank are integratedinto a one-piece lens.

In one preferable embodiment of the invention, the second lens blank ischaracterized by having shading capability.

In another preferable embodiment of the invention, the second lens blankis characterized by being a metal, cermet or ceramics.

Yet another embodiment of the invention is characterized in that anorganic-inorganic composite lens blank is used as an optical lens blankfor at least one optical element that forms a part of the opticalsystem.

Further, the invention includes an electronic system comprising theabove zoom optical system and an electronic image pickup device locatedon an image side thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is generally illustrative of how to fabricate the one-piece lensfor use with the invention. FIG. 1( a) is illustrative of how a lensblank is located before lens molding, and FIG. 1( b) is illustrative ofhow the lens blank is molded into the one-piece lens after lens molding.

FIG. 2 is a perspective view of the one-piece lens molded by thefabrication process of FIG. 1.

FIG. 3 is generally illustrative of another fabrication process of theone-piece lens for use with the zoom optical system. FIG. 3( a) isillustrative of how lens blanks are located before lens molding, andFIG. 3( b) is illustrative of how the lens blanks are molded into theone-piece lenses after lens molding.

FIG. 4 is illustrative in perspective of a one-piece lens fabricated bythe fabrication process of FIG. 2.

FIG. 5 is generally illustrative of yet another fabrication process ofthe one-piece lens for use with the zoom optical system. FIG. 5( a) isillustrative of how lens blanks are located before lens molding, andFIG. 5( b) is illustrative of how the lens blanks are molded into theone-piece lenses after lens molding.

FIG. 6 is illustrative in perspective of a one-piece lens fabricated bythe fabrication process of FIG. 5.

FIG. 7 is illustrative in lens section of Example 1-1 of the first zoomoptical system, showing lens sections at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 8 is illustrative in lens section of Example 1-2 of the first zoomoptical system, showing lens sections at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 9 is an aberration diagram for Example 1-1 of the first zoomoptical system, showing aberrations at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 10 is an aberration diagram for Example 1-2 of the first zoomoptical system, showing aberrations at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 11 is illustrative in section of one exemplary one-piece lens usedin Example 1-1 of the first zoom optical system.

FIG. 12 is illustrative in section of one exemplary one-piece lens usedin Example 1-2 of the first zoom optical system.

FIG. 13 is illustrative in section of another exemplary one-piece lensused in Example 1-2 of the first zoom optical system.

FIG. 14 is illustrative in lens section for Example 2-1 of the secondzoom optical system, showing aberrations at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 15 is illustrative in lens section for Example 2-2 of the secondzoom optical system, showing aberrations at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 16 is an aberration diagram for Example 2-1 of the second zoomoptical system, showing aberrations at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 17 is an aberration diagram for Example 2-2 of the second zoomoptical system, showing aberrations at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 18 is illustrative in section of one exemplary one-piece lens usedin Example 2-1 of the second zoom optical system.

FIG. 19 is illustrative in section of one exemplary one-piece lens usedin Example 2-2 of the second zoom optical system.

FIG. 20 is illustrative in lens section of Example 3-1 of the third zoomoptical system, showing lens sections at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 21 is illustrative in lens section of Example 3-2 of the third zoomoptical system, showing lens sections at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 22 is an aberration diagram for Example 3-1 of the third zoomoptical system, showing aberrations at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 23 is an aberration diagram for Example 3-2 of the third zoomoptical system, showing aberrations at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 24 is illustrative in section of one exemplary one-piece lens usedin Example 3-1 of the third zoom optical system.

FIG. 25 is illustrative in section of one exemplary one-piece lens usedin Example 3-2 of the third zoom optical system.

FIG. 26 is illustrative in lens section of Example 4-1 of the fourthzoom optical system, showing lens sections at a wide-angle end (a), inan intermediate setting (b) and at a telephoto end (c) upon focusing onan infinite object point.

FIG. 27 is illustrative in lens section of Example 4-2 of the fourthzoom optical system, showing lens sections at a wide-angle end (a), inan intermediate setting (b) and at a telephoto end (c) upon focusing onan infinite object point.

FIG. 28 is an aberration diagram for Example 4-1 of the fourth zoomoptical system, showing aberrations at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 29 is an aberration diagram for Example 4-2 of the fourth zoomoptical system, showing aberrations at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 30 is illustrative in section of one exemplary one-piece lens usedin Example 4-1 of the fourth zoom optical system.

FIG. 31 is illustrative in section of one exemplary one-piece lens usedin Example 4-2 of the fourth zoom optical system.

FIG. 32 is illustrative in lens section of Example 5-1 of the fifth zoomoptical system, showing lens sections at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 33 is illustrative in lens section of Example 5-2 of the fifth zoomoptical system, showing lens sections at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 34 is an aberration diagram for Example 5-1 of the fifth zoomoptical system, showing aberrations at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 35 is an aberration diagram for Example 5-2 of the fifth zoomoptical system, showing aberrations at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 36 is illustrative in section of one exemplary one-piece lens usedin Example 5-1 of the fifth zoom optical system.

FIG. 37 is illustrative in section of one exemplary one-piece lens usedin Example 5-2 of the fifth zoom optical system.

FIG. 38 is illustrative in lens section of Example 6-1 of the sixth zoomoptical system, showing lens sections at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 39 is illustrative in lens section of Example 6-2 of the sixth zoomoptical system, showing lens sections at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 40 is illustrative in lens section of Example 6-3 of the sixth zoomoptical system; showing lens sections at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 41 is an aberration diagram for Example 6-1 of the sixth zoomoptical system, showing aberrations at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 42 is an aberration diagram for Example 6-2 of the sixth zoomoptical system, showing aberrations at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 43 is an aberration diagram for Example 6-3 of the sixth zoomoptical system, showing aberrations at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 44 is illustrative in section of one exemplary one-piece lens usedin Example 6-1 of the sixth zoom optical system.

FIG. 45 is illustrative in section of one exemplary one-piece lens usedin Example 6-2 of the sixth zoom optical system.

FIG. 46 is illustrative in section of one exemplary one-piece lens usedin Example 6-3 of the sixth zoom optical system.

FIG. 47 is illustrative in lens section of Example 7-1 of the seventhzoom optical system, showing lens sections at a wide-angle end (a), inan intermediate setting (b) and at a telephoto end (c) upon focusing onan infinite object point.

FIG. 48 is illustrative in lens section of Example 7-2 of the seventhzoom optical system, showing lens sections at a wide-angle end (a), inan intermediate setting (b) and at a telephoto end (c) upon focusing onan infinite object point.

FIG. 49 is illustrative in lens section of Example 7-3 of the seventhzoom optical system, showing lens sections at a wide-angle end (a), inan intermediate setting (b) and at a telephoto end (c) upon focusing onan infinite object point.

FIG. 50 is an aberration diagram for Example 7-1 of the seventh zoomoptical system, showing aberrations at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 51 is an aberration diagram for Example 7-2 of the seventh zoomoptical system, showing aberrations at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 52 is an aberration diagram for Example 7-3 of the seventh zoomoptical system, showing aberrations at a wide-angle end (a), in anintermediate setting (b) and at a telephoto end (c) upon focusing on aninfinite object point.

FIG. 53 is illustrative in section of one exemplary one-piece lens usedin Example 7-1 of the seventh zoom optical system.

FIG. 54 is illustrative in section of one exemplary one-piece lens usedin Example 7-2 of the seventh zoom optical system.

FIG. 55 is illustrative in section of another exemplary one-piece lensused in Example 7-2 of the seventh zoom optical system.

FIG. 56 is illustrative in section of one exemplary one-piece lens usedin Example 7-3 of the seventh zoom optical system.

FIG. 57 is a front perspective view of the appearance of a digitalcamera with a built-in inventive zoom optical system.

FIG. 58 is a rear perspective view of the digital camera of FIG. 57.

FIG. 59 is a sectional view of the digital camera of FIG. 57.

FIG. 60 is a front perspective view of a personal computer with a coverheld open, wherein the zoom optical system of the invention isincorporated in the form of an objective optical system.

FIG. 61 is a sectional view of a taking optical system in the personalcomputer.

FIG. 62 is a side view of the taking optical system in the state of FIG.60.

FIGS. 63( a) and (b) are a front view and a side view of a cellularphone wherein the zoom optical systems of the invention is incorporatedin the form of an objective optical system, and FIG. 63( c) is asectional view of a taking optical system in it.

BEST MODES OF CARRYING OUT THE INVENTION

The present invention provides a zoom optical system comprising a lensgroup having negative refracting power and a lens group having positiverefracting power, wherein at least one lens is formed by molding of afirst lens blank that provides a surface including at least an opticalfunction surface after molding, and a second lens blank that provides asurface other than said surface including at least an optical functionsurface after molding, and the first lens blank and the second lensblank are integrated into a one-piece lens.

A zoom optical system may generally be broken down into the followingseven types:

(1) the first group is a negative lens group, and the second group is apositive lens group;

(2) the first group is a positive lens group, and the second group is anegative lens group;

(3) the first group is a negative lens group, the second group is apositive lens group, and the third group is a positive lens group;

(4) the first group is a negative lens group, the second group is apositive lens group, the third group is a positive lens group, and thefourth group is a negative lens;

(5) the first group is a negative lens group, the second group is apositive lens group, the third group is a negative lens group, and thefourth group is a positive lens group;

(6) the first group is a negative lens group, the second group is apositive lens group, the third group is a positive lens group, and thefourth group is a positive lens group; and

(7) the first group is a positive lens group, the second group is anegative lens group, the third group is a positive lens group, and thefourth group is a positive lens group.

Each type will be described at great length later.

In such zoom optical systems, at least one one-piece lens shouldpreferably satisfy the following condition (1) with respect to thethickness of its thinnest portion.0.1 mm<t<0.5 mm  (1)Here t is the thickness of the thinnest portion of the one-piece lens.

The advantage of, and the requirement for, the above arrangement is nowexplained. The reduction in the thickness of the thinnest portion of theone-piece lens enables it to be formed so small that the total length ofthe lens system can be made short. In other words, the satisfaction ofcondition (1) ensures that size reductions are achievable while opticalperformance is kept intact. As the lower limit of 0.1 mm to condition(1) is not reached, the lens becomes too thin to stand up deformationdue to external pressure, temperature, etc., having difficulty inkeeping the optical performance. Exceeding the upper limit of 0.5 mmcauses the thinnest portion to become large, rendering the lens large.

More preferably, the following condition (1-2) should be satisfied, sothat the optical system can be more slimmed down while the opticalperformance is maintained.0.15 mm<t<0.4 mm  (1-2)

Even more preferably, the following condition (1-3) should be satisfied,so that the optical system can be much more slimmed down while theoptical performance is maintained.0.2 mm<t<0.35 mm  (1-3)

For the one-piece lens that satisfies the above conditions, it is alsopreferable to have positive refracting power.

The advantage of, and the requirement for, this arrangement is nowexplained. With the positive lens formed as a one-piece lens, its edgethickness difference can be diminished, resulting in a decrease in thetotal length of the lens system.

When the one-piece lens is molded, it is preferable to simultaneouslyform a plurality of optical function surfaces on a single moldingmachine.

The advantage of, and the requirement for, this arrangement is nowexplained. Simultaneous formation of a plurality of parallel opticalfunction surfaces on a single molding machine allows for a reduction inthe processing time for each surface, and ensues as well that theservice life of a press per the number of surfaces is extended.Therefore, some significant cost reductions are achievable.

Preferably, the first lens blank should be a glass.

The advantage of, and the requirement for, this arrangement is nowexplained. Use of a high-refractive-index glass as the first lens blankallows for satisfactory correction of various aberrations such asspherical aberrations and field curvature with a fewer lenses. The glassis less susceptible of influences of temperature changes. It is thuspossible to achieve an optical system that has limited back focusfluctuations with temperature changes. It is understood that plastic ororganic-inorganic composite lens blanks could be used as the first lensblank.

Preferably, the second lens blank should have shading capability.

The advantage of, and the requirement for, this arrangement is nowexplained. With the shading capability of the second lens blank, lightrays coming from surfaces other than the optical function surfacearriving at the image plane can be so minimized that ghost light andflare light can be prevented.

Preferably, the second lens blank should be a metal, cermet or ceramics.

The advantage of, and the requirement for, this arrangement is nowexplained. If the second lens blank is a metal, cermet (a ceramic-metalcomposite lens blank) or ceramics, shaping is easily achievable.

Preferably, an organic-inorganic composite lens blank should be used asan optical lens blank for at least one optical element that forms a partof the optical system.

The advantage of, and the requirement for, this arrangement is nowexplained. As the organic-inorganic composite material is used as theoptical material of an optical element, it allows various opticalproperties (refractive index, chromatic dispersion) to show up (or beobtained) depending on the types and content ratios of the organic andinorganic components. Thus, if the organic and inorganic components areblended at any desired ratio, it is then possible to achieve opticalmaterials having the desired, or higher, optical properties. This inturn enables an optical element having ever high performance to be soobtained that various aberrations can be corrected with a fewer lenses,resulting in cost savings and size reductions of an optical system.

Preferably, the organic-inorganic composite material should containzirconia in a nano-particle form.

Preferably, the organic-inorganic composite material should containzirconia and alumina in a nano-particle form.

Preferably, the organic-inorganic composite material should contain aniobium oxide in a nano-particle form.

Preferably, the organic-inorganic composite material should contain azirconium alkoxide hydrolyzate and alumina in a nano-particle form.

The advantage of, and the requirement for, this arrangement is nowexplained. These inorganic materials in a nano-particle form areexamples of the inorganic component. If such nano-particles aredispersed through the organic component, typically a plastic componentat a given ratio, various optical properties (refractive index,chromatic dispersion) can then be developed.

How to fabricate the one-piece lens is explained with reference toFIG. 1. Referring to FIG. 1( a), reference numerals 14 and 15 representa bottom force and a top force of a one-piece lens molding press,respectively. At a given area of the bottom force 14, there is provideda one-piece lens bottom surface dish (hereinafter called simply thebottom surface dish), which corresponds to an optical function surfaceportion of the post-molding one-piece lens. At a given area of the topforce 15, too, there is provided a one-piece lens top cavity(hereinafter called simply the top surface cavity), which corresponds toan optical function surface portion of the post-molding one-piece lens.

A one-piece lens 10 is molded of a first lens blank 11 and a second lensblank 12. The first lens blank 11 is to be provided with a surfaceincluding at least an optical function surface after the formation ofthe one-piece lens by molding, and the second lens blank 12 is to beprovided with a surface other than the surface including at least anoptical function surface after the formation of the one-piece lens bymolding. This surface other than the surface including an opticalfunction surface is formed at and around the surface formed by the firstlens blank 11. For instance, this surface is to provide a surface tocontact a lens barrel to support the one-piece lens or a centeringsurface.

The second lens blank 12 is provided with a cavity 13. Therefore, whenthe one-piece lens 10 is fabricated, the first lens blank 11 is placedtogether with the second lens blank 12 on the bottom force 14 of theone-piece lens molding press, as shown in FIG. 1( a), while the firstlens blank 11 is fitted into the cavity 13. In this state, the firstlens blank 11 is heated to a temperature at which it is deformable, andwhich could be a suitable temperature higher than the transition pointof the first lens blank 11. Then, when the suitable temperature isreached, the top force 15 of the one-piece lens molding press goes downfrom above until it contacts the surface of the second lens blank 12.This permits the first lens blank 11 to be pressed by the bottom and topforces. As a result, the first lens blank 11 is molded into a formcommensurate with the bottom and top forces, providing the one-piecelens 10, as shown generally in FIG. 1( b).

After removal of the top force 15 of FIG. 1( b), the one-piece lens 10is easily released from within the bottom force 14. In the one-piecelens 10, the first lens blank 11 is integrally fused to the cavity inthe second lens blank 12, as shown in the perspective view of FIG. 2. InFIG. 1, a set of the first and second lens blanks 11 and 12 are placedin a pair of forces 14 and 15 by way of illustration alone. Anotherembodiment of this arrangement is now explained.

In another embodiment of FIG. 3, a pair of bottom force 14 and top force15 of a molding press are provided with a plurality of dishes in aparallel fashion. A plurality of the first and second lens blanks 11 and12 are located in correspondence to the respective dishes. Thus, aplurality of one-piece lenses are simultaneously molded. In FIG. 3( a),reference numerals 14 and 15 are the bottom and top forces of theone-piece lens molding press. At a given area of the bottom force 14,there are provided a plurality of one-piece lens bottom surface dishes(hereinafter called simply the bottom surface dishes). These bottomsurface dishes are each to provide an optical function surface portionof the post-molding one-piece lens. At a given area of the top force 15,too, there are provided a plurality of one-piece lens top surface dishes(hereinafter called simply the top surface dishes). These top surfacedishes, too, are each to provide an optical function surface portion ofthe post-molding one-piece lens.

As shown in FIG. 3( a), the one-piece lens of this embodiment, too, ismolded of the first lens blank 11 and the second lens blank 12. Thefirst lens blank 11 is to provide a surface including at least anoptical function surface after the formation of an individual one-piecelens by molding, and the second lens blank 12 is to provide a surfaceother than the surface including at least an optical function surfaceafter the formation of an individual one-piece lens by molding. Thissurface other than the surface including an optical function surface isformed at and around the surface formed by the first lens blank 11. Forinstance, this surface is to provide a surface to contact a lens barrelto support the one-piece lens or a centering surface.

The second lens blank 12 is provided with a plurality of cavities 13. Inthis embodiment, therefore, one-piece lenses are formed in an arrayfashion. Then, one-piece lenses 10′ formed in an array fashion(hereinafter called the array lenses 10′) are individually cut off toobtain individual one-piece lenses 10 as shown in FIG. 2. For thefabrication of the array lenses 10′, a plurality of the first lensblanks 11 are placed together with the second lens blank 12 on thebottom force 14 of the one-piece lens molding press, while the firstlens blanks 11 are each fitted into the cavity 13. In this state, thefirst lens blanks 11 are heated to a temperature at which they aredeformable, and which could be a suitable temperature higher than theirtransition point. Then, when the suitable temperature is reached, thetop force 15 of the one-piece lens press goes down from above until itcontacts the surface of the second lens blank 12. This permits the firstlens blanks 11 to be each pressed by the bottom and top forces. As aresult, the first lens blanks 11 are formed in a form commensurate withthe bottom and top dishes, giving the array lenses 10′, as showngenerally in FIG. 3( b).

In this embodiment, rims 16 are provided on the top force 15, as shownin FIG. 3. The rims 16 are transferred onto the second lens blank in aslot form simultaneously with molding. After removal of the top force 15of FIG. 3( b), the array lenses 10′ are easily released from within thebottom force 14. In these array lenses 10′, the first lens blanks 11 areeach integrally fused to the cavity 13 in the second lens blank 12.Thereafter, the second lens blank 12 is cut off to obtain a plurality ofone-piece lenses 10. In FIGS. 3 and 4, a 3×3 lens array is shown;however, how many lenses are to be obtained is not critical.

Yet another embodiment is shown in FIGS. 5 and 6. This embodiment isdifferent from the embodiment of FIGS. 3 and 4 only in that there are norims 16 on the top force 15. Thus, the second lens blank 12 has no slots17.

Each type of the zoom optical system is now explained.

(1) First of all, reference is made to the type wherein the first groupis a negative lens group and the second group is a positive lens group.

The first zoom optical system of the invention comprises, in order fromits object side, a first group having negative refracting power and asecond group having positive refracting power, wherein at least one lensis formed by molding of a first lens blank that provides a surfaceincluding at least an optical function surface after molding and asecond lens blank that provides a surface other than the surfaceincluding at least an optical function surface after molding. In otherwords, at least one lens comprises a one-piece lens wherein the firstlens blank and the second lens blank are integrated together.

The advantage of, and the requirement for, the above arrangement is nowexplained. Such a zoom optical system of negative-positive groupconstruction can be set up with a reduced number of lenses, and so isbest suited for size reductions and cost savings. With the one-piecelens, further size reductions are achievable. This is because for theone-piece lens any peripheral thickness for rounding is not required,when compared with the prior art lens processing, as described justbelow.

For the prior art lens processing, rounding is essential. For thisreason, the outer peripheral portion of a lens prior to rounding musthave some thickness or edge thickness difference, resulting in anincreased center thickness (the thickness of a center portion). However,the one-piece lens for use with the first zoom optical system has alimited edge thickness difference, so that the optical system can bediminished in total length. With the prior art lens processing, thestronger the power of a positive lens, the larger the thickness of itsouter peripheral portion becomes at the necessary outer diameter. Forthe first zoom optical system, however, it is not necessary to ensurethe thickness of the outer peripheral portion at the time of rounding.Therefore, the stronger the power of the positive lens, the moresignificant the effect on size reductions becomes.

Such a one-piece lens is also easy to handle, leading to savings of thecost for zoom lens system fabrication.

With the first zoom optical system, zooming from its wide-angle end toits telephoto end, for instance, is carried out as follows. The firstgroup moves in a concave locus toward the object side, and the secondlens group moves toward the object side.

Preferably for the first zoom optical system, the one-piece lens shouldbe cemented to other lens.

The advantage of, and the requirement for, the above arrangement is nowexplained. If the one-piece lens is cemented to other lens as mentionedabove, the sensitivity to decentration (decentration errors) can then bemore reduced as compared with the case where individual lenses areindependently assembled. Therefore, setting up the optical systembecomes easy, leading to low costs.

Preferably for the first zoom optical system, at least one opticalfunction surface of the one-piece lens should be an aspheric surface. Toput it another way, the one-piece lens should be an aspheric one-piecelens.

The advantage of, and the requirement for, the above arrangement is nowexplained. The use of such an aspheric surface ensures that variousaberrations are held back, with the result that the number of lenses inthe whole system can be diminished, and size reductions and cost savingsare achievable as well.

Preferably for the first zoom optical system, the first group shouldcomprise at least one positive lens.

The advantage of, and the requirement for, the above arrangement is nowexplained. The first group, because of having negative power, includesat least one negative lens. Therefore, if the positive lens isincorporated in the first group, it is then possible to hold backfluctuations with zooming of various aberrations inclusive of sphericalaberrations, coma and chromatic aberration of magnification.

Preferably for the first zoom optical system, the first group shouldinclude a negative lens nearest to its object side.

The advantage of, and the requirement for, the above arrangement is nowexplained. With this arrangement, the effective diameter of the lensesin the first group and the total length of the lens system can beshortened.

Preferably for the first zoom optical system, the first group shouldcomprise at least one one-piece lens.

The advantage of, and the requirement for, the above arrangement is nowexplained. Because the lenses in the first group have a large effectivediameter, there is an increase in the volume necessary for it.Therefore, if the one-piece lens is used for any of the lenses in thefirst group, the volume of the optical material can then be diminished.As a result, cost reductions are achievable.

Also, because the volume of the lenses themselves becomes small, theoptical system can be slimmed down. Further, because the one-piece lensis easy to handle, the cost for the fabrication of the optical systemcan be cut short.

Preferably for the first zoom optical system, at least one of theone-piece lenses in the first group should have positive refractingpower.

The advantage of, and the requirement for, the above arrangement is nowexplained. For correction of chromatic aberration of magnification,etc., it is preferable to locate a positive lens in the first group.Here, if a one-piece lens is used as this positive lens, it is thenpossible to make the edge thickness difference of the positive lenssmall and, hence, shorten the total length of the lens system.

Preferably for the positive lens in the first group, it is preferable touse a high-refractive-index, high-dispersion optical material for thepurpose of correcting chromatic aberration of magnification, andspherical aberrations, etc. at the telephoto end. It is generally notedthat the high-refractive-index, high-dispersion material costs much. Toadd up to this, for the positive lens in the first lens group, it isrequired to have a large volume, because of its large effectivediameter. Here, if a one-piece lens is used as this positive lens, it isthen possible to decrease the volume of the optical material necessaryfor the positive lens. Therefore, cost reductions are achievable.Further, the volume of the lens itself becomes small, and so the opticalsystem can be slimmed down.

Preferably for the first zoom optical system, at least one positive lensin the first group should satisfy the following condition.0.1<HH1/φ1<10  (2A)Here, HH1 is the principal point spacing (mm) of the positive lens inthe first group, and φ1 is the refracting power of the positive lens inthe first group.

The advantage of, and the requirement for, the above arrangement is nowexplained. With a negative lens located in the first group (and nearestto its object side), there is chromatic aberration of magnification. Tocorrect the chromatic aberration of magnification, etc. with a fewerlenses, i.e., at low costs, it is preferable to have a positive lens ofincreased power in the first group.

With the prior art lens processing, however, a lens is formed somewhatlarger than the necessary outer diameter, and rounding is carried out insuch a way as to incorporate it in a lens barrel. For this reason, whena positive lens is formed by molding, the thickness of its outerperipheral portion at the necessary outer diameter becomes larger thanthat of the lens at the time of rounding. Further, as the power of thepositive lens increases, the thickness of the outer peripheral portionat the necessary outer diameter becomes far larger because of the needof ensuring the outer peripheral thickness of the lens at the time ofrounding. As a result, it is difficult to make a sensible compromisebetween the reduction in the whole lens length and the size reduction ofeach lens or between cost savings and size reductions.

However, if a one-piece lens is used as the positive lens in the firstgroup, it is unnecessary to form the positive lens larger than thenecessary outer diameter, and the satisfaction of condition (2A) enableslarge power to be achieved with a thin lens. It is thus possible toachieve cost savings and size reductions at the same time.

As the lower limit of 0.1 to condition (2A) is not reached, the powerbecomes too large relative to the principal point spacing. This does notonly result in an increased sensitivity to decentration, but also hasdifficulty in keeping the optical performance intact. As the upper limitof 10 is exceeded, the power becomes small relative to the principalpoint spacing. Thus, chromatic aberration of magnification or the likeproduced at the negative lens in the first group remains undercorrected.Alternatively, more lenses must be used for correction of chromaticaberration of magnification or the like.

More preferably,0.5<HH1/φ1<6  (2A-2)In this case, the optical system can be more slimmed down at the samelow cost.

Even more preferably,1<HH1/φ1<3  (2A-3)In this case, the optical system can be much more slimmed down at thesame low cost.

Preferably for the first zoom optical system, at least one one-piecelens in the first group should have at least one aspheric surface.

The advantage of, and the requirement for, the above arrangement is nowexplained. At the wide-angle end of the first zoom optical system, lightrays gain height at the first group. For this reason, it is preferableto include at least one aspheric surface in the first group. This allowsfor good correction of off-axis aberrations such as astigmatism,distortion and coma with a fewer lenses. Therefore, the optical systemcan be reduced in terms of both size and cost.

At the telephoto end, the diameter of a light beam through the firstgroup grows large. Therefore, if at least one aspheric surface isincluded in the first group, spherical aberrations, coma, etc. can thenbe well corrected with a fewer lenses. In this case, too, the opticalsystem can be reduced in terms of both size and cost.

Preferably for the first zoom optical system, the second group shouldcomprise at least one negative lens.

The advantage of, and the requirement for, the above arrangement is nowexplained. The second group, because of having positive power, comprisesat least one positive lens. Therefore, if it includes a negative lens,fluctuations with zooming of various aberrations such as coma,astigmatism and longitudinal chromatic aberration can then be held back.

Preferably for the first zoom optical system, the second group shouldhave a positive lens located nearest to its object side.

The advantage of, and the requirement for, the above arrangement is nowexplained. At the second group, it is required to converge lightdiverged at the first group of negative power. Thus, the lens locatednearest to the object side should preferably be a positive lens.

Preferably for the first zoom optical system, the second lens groupshould have a negative lens located nearest to its image side.

The advantage of, and the requirement for, the above arrangement is nowexplained. The location of the negative lens nearest to the image sideof the second group provides the two following advantages: (1) theprincipal point position displaces toward the first group side, so thatthe principal point spacing between the first group and the second groupcan be shortened, resulting in a decrease in the total length of thelens system; and (2) the second group is so increased in terms ofmagnification that the amount of movement of the second group withzooming can be decreased, resulting in a decrease in the total length.

Preferably for the first zoom optical system, the second group shouldcomprise at least one one-piece lens and at least one of one-piecelenses should have positive refracting power.

The advantage of, and the requirement for, the above arrangement is nowexplained. The use of the one-piece lens as the positive lens allows fora decrease in the edge thickness difference of the positive lens, withthe result that the whole length of the lens system can be shortened.

The positive lens in the second group should also preferably be formedof a high-refractive-index, low-dispersion optical material for thepurpose of holding back longitudinal chromatic aberration, sphericalaberration, astigmatism, etc. Commonly, however, thehigh-refractive-index, low-dispersion optical material costs much.Therefore, it is preferable to use a one-piece lens for that positivelens, because the volume of the optical material necessary for thepositive lens can be reduced and, hence, cost can be cut short.

Further, the volume of the lens itself becomes so small that the opticalsystem can be slimmed down. Furthermore, since that one-piece lens iseasy to handle, it is possible to cut short the cost for the fabricationof the zoom optical system.

Preferably for the first zoom optical system, at least one positive lensin the second group should satisfy the following condition.0.1<HH2/φ2<10  (3A)Here, HH2 is the principal point spacing (mm) of the positive lens inthe second group, and φ2 is the refracting power of the positive lens inthe second group.

The advantage of, and the requirement for, the above arrangement is nowexplained. By increasing the power of the positive lens located in thesecond group, the distance of movement of the second group can be madeshort. This leads to a reduction in the whole length of the lens system.However, the prior art lens processing has difficulty in reconciling thereduction in the whole length of the lens system with slimming down eachlens, as already detailed with reference to condition (2A).

However, if that positive lens is molded as a one-piece lens, it is thenunnecessary to form it larger than the necessary outer diameter. Thesatisfaction of condition (3A) enables large power to be achieved with athin lens. In this way, further size reductions are achievable.

As the lower limit of 0.1 to condition (3A) is not reached, the powerbecomes too large relative to the principal point spacing. This does notonly result in an increased sensitivity to decentration, but also hasdifficulty in keeping the optical performance intact. As the upper limitof 10 is exceeded, the power becomes small relative to the principalpoint spacing, failing to decrease the amount of movement of the secondgroup, and resulting in an increase in the whole length of the lenssystem.

It is more preferable to satisfy the following condition (3A-2), becausethe reduction in the whole length of the lens system can be reconciledwith slimming down each lens.0.5<HH2/φ2<2  (3A-2)

It is even more preferable to satisfy the following condition (3A-2),because the tradeoff between the reduction in the whole length of thelens system and slimming down each lens is more easily achievable.1<HH2/φ2<1.5  (3A-3)

Preferably for the first zoom optical system, at least one one-piecelens in the second group should be cemented to other lens.

The advantage of, and the requirement for, the above arrangement is nowexplained. The incorporation of a cemented lens in the second groupallows for a decrease in the sensitivity to decentration, which in turnmakes the assembling of the optical system easy, leading to costsavings.

Preferably for the first zoom optical system, at least one one-piecelens in the second group should have at least one aspheric surface.

The advantage of, and the requirement for, the above arrangement is nowexplained. The first group has negative refracting power. In this case,a light beam is enlarged through the first group into a light beam oflarger diameter, which is then incident on the second group. Thus, thelight beam through the second group has a larger diameter, and if atleast one aspheric surface is introduced in the second group, goodaberration correction can be made. For lens diameter reductions, thepower of each group must be increased. As the positive power of thesecond group increases, however, there are large transversemagnification and aberration changes of the second group with zooming.If the aspheric surface is introduced in the second group, it ispossible to make correction for aberrations produced at the second groupand hold back aberration fluctuations with zooming.

(2) Reference is then made to the type wherein the first group is apositive lens group and the second group is a negative lens group.

The second zoom optical system of the invention comprises, in order fromits object side, a first group having positive refracting power and asecond group having negative refracting power, wherein at least one lensis formed by molding of a first lens blank that provides a surfaceincluding at least an optical function surface after molding and asecond lens blank that provides a surface other than the surfaceincluding at least an optical function surface after molding. In otherwords, at least one lens comprises a one-piece lens wherein the firstlens blank and the second lens blank are integrated together.

The advantage of, and the requirement for, the above arrangement is nowexplained. As in the zoom optical system of negative-positive groupconstruction, the zoom optical system of such negative-positive groupconstruction can be set up with a reduced number of lenses, and so isbest suited for size reductions and cost savings. With the one-piecelens, further size reductions are achievable. This is because for theone-piece lens any peripheral thickness for rounding is not required,when compared with the prior art lens processing, as previouslydescribed in conjunction with the first zoom optical system.

Such a one-piece lens is also easy to handle, leading to savings of thecost for zoom lens system fabrication.

Here, with the second zoom optical system, zooming from the wide-angleend to the telephoto end, for instance, is carried out as described justbelow. The first group and the second group move to the object side ofthe optical system while the space between the first group and thesecond group becomes narrow.

Preferably for the second zoom optical system, the one-piece lens shouldbe cemented to other lens, and at least one optical function surfaceshould be an aspheric surface. In other words, the one-piece lens shouldpreferably be an aspheric one-piece lens.

The advantage of, and the requirement for, the above arrangement is thesame as in the first zoom optical system.

Preferably for the second zoom optical system, the first group shouldcomprise at least one negative lens.

The advantage of, and the requirement for, the above arrangement is nowexplained. The first group, because of having positive power, includesat least one positive lens. Therefore, if the negative lens isincorporated in the first group, it is then possible to hold backfluctuations with zooming of various aberrations inclusive of sphericalaberration, coma and chromatic aberration of magnification.

Preferably for the second zoom optical system, the first group shouldinclude a positive lens nearest to its image side.

The advantage of, and the requirement for, the above arrangement is nowexplained. The location of the positive lens nearest to the image sideof the first group allows for a decrease in the spacing between the rearprincipal point of the first group and the front principal point of thesecond group, resulting in the achievement of size reductions.

Preferably for the second zoom optical system, the first group shouldcomprise at least one one-piece lens, wherein the one-piece lens is apositive lens.

The advantage of, and the requirement for, the above arrangement is thesame as in the first zoom optical system. The use of the one-piece lensas the positive lens enables the edge thickness difference of thepositive lens to become small. Therefore, the whole length of the lenssystem can be shortened.

Preferably for the second zoom optical system, the positive lens in thefirst group should satisfy the following condition.0.1<HH1/φ1<15  (2B)Here, HH1 is the principal point spacing (mm) of the positive lens inthe first group, and φ1 is the refracting power of the positive lens inthe first group.

The advantage of, and the requirement for, the above arrangement is nowexplained. In order from the optical system to be of a telephoto typehaving a shortened total length, it is preferable that the positive lensin the first group have large power. However, the prior art lensprocessing has difficulty in offering a sensible tradeoff between lowcost and slimming-down, as already detailed in conjunction with thefirst zoom optical system.

However, if a one-piece lens is used as the positive lens in the firstgroup, it is unnecessary to form the positive lens larger than thenecessary outer diameter, and the satisfaction of condition (2B) enableslarge power to be achieved with a thin lens. It is thus possible toachieve cost savings and size reductions at the same time.

As the lower limit of 0.1 to condition (2B) is not reached, the powerbecomes too large relative to the principal point spacing. This does notonly result in an increased sensitivity to decentration, but also hasdifficulty in keeping the optical performance intact. As the upper limitof 15 is exceeded, the effect of the telephoto type becomes slender,because the power becomes small relative to the principal point spacing.Therefore, the whole length of the lens system becomes long.Alternatively, a lot more lenses must be used for setting up thetelephoto type.

It is more preferable to satisfy the following condition (2B-2). In thiscase, the reduction in the whole length of the lens system and slimmingdown each lens are achievable at the same time.0.5<HH1/φ1<6  (2B-2)

It is even more preferable to satisfy the following condition (2B-3). Inthis case, it is easier to achieve the reduction in the whole length ofthe lens system and slimming down each lens at the same time.1<HH1/φ1<2  (2B-3)

Preferably for the second zoom optical system, at least one one-piecelens in the first group should be cemented to other lens.

The advantage of, and the requirement for, the above arrangement is nowexplained. By the incorporation of such a cemented lens in the firstgroup, the sensitivity to decentration can be so diminished that theassembling of the optical system is facilitated, leading to costsavings.

Preferably for the second zoom optical system, at least one one-piecelens in the first group should has at least one aspheric surface.

The advantage of, and the requirement for, the above arrangement is nowexplained. In the zoom optical system of positive-negative groupconstruction, there is a large light beam diameter at the first group.Therefore, if at least one aspheric surface is included in the firstgroup, spherical aberration, coma or other aberrations can then be wellcorrected.

Preferably for the second zoom optical system, the second group shouldcomprise at least one positive lens.

The advantage of, and the requirement for, the above arrangement is nowexplained. At the wide-angle end of the zoom optical system ofpositive-negative group construction, light rays gain height at thesecond group. Therefore, if at least one positive lens is included inthe second group, fluctuations with zooming of various aberrations suchas astigmatism and chromatic aberration of magnification can then beheld back.

At the telephoto end, a light beam through the second group has a largediameter. Therefore, if at least one positive lens is introduced in thesecond group, fluctuations with zooming of spherical aberration, coma,etc. can then be held back.

Preferably for the second zoom optical system, the second group shouldhave a negative lens nearest to its image side.

The advantage of, and the requirement for, the above arrangement is nowexplained. The location of the negative lens nearest to the image sideof the second group provides the two following advantages: (1) theprincipal point position displaces toward the first group side, so thatthe principal point spacing between the first group and the second groupcan be shortened, resulting in a decrease in the total length of thelens system; and (2) the second group is so increased in terms ofmagnification that the amount of movement of the second group withzooming can be decreased, resulting in a decrease in the total length.

Preferably for the second zoom optical system, the second group shouldcomprise at least one one-piece lens.

The advantage of, and the requirement for, the above arrangement is nowexplained. The second group, because of having a large effectivediameter, grows large in terms of the necessary volume. Therefore, ifthe one-piece lens is used for the lens in the second group, the volumeof the optical material can then be diminished, resulting in costsavings.

Also, because the volume of the one-piece lens itself becomes small, theoptical system can be slimmed down. In addition, the one-piece lens isso easy to handle that the cost for the fabrication of the opticalsystem can be cut short.

Preferably for the second zoom optical system, at least one of theone-piece lenses in the second group should be a positive lens.

The advantage of, and the requirement for, the above arrangement is nowexplained. If the one-piece lens is used as the positive lens, the edgethickness difference of the positive lens can then be diminished,resulting in a reduction in the whole length of the lens system.

The positive lens in the second group should also preferably be formedof a high-refractive-index, low-dispersion optical material for thepurpose of holding back chromatic aberration of magnification, sphericalaberration, etc. Commonly, however, the high-refractive-index,low-dispersion optical material costs much. In addition, to be moreeffective, the positive lens in the second group increases in thenecessary volume. Therefore, it is preferable to use a one-piece lensfor that positive lens, because the volume of the optical materialnecessary for the positive lens can be reduced and, hence, cost can becut short.

Further, the volume of the lens itself becomes so small that the opticalsystem can be slimmed down. Furthermore, since that one-piece lens iseasy to handle, it is possible to cut short the cost for the fabricationof the zoom optical system.

Preferably for the second zoom optical system, at least one positivelens in the second group should satisfy the following condition.0.1<HH2/φ2<6  (3B)Here, HH2 is the principal point spacing (mm) of the positive lens inthe second group, and φ2 is the refracting power of the positive lens inthe second group.

The advantage of, and the requirement for, the above arrangement is nowexplained. By increasing the power of the positive lens located in thesecond group, the lens system is permitted to be of the telephoto type,leading to a decrease in the whole length of the lens system. At thewide-angle end, astigmatism and chromatic aberration of magnificationfluctuations with zooming are well correctable with a fewer lenses, andat the telephoto end, fluctuations with zooming of various aberrationssuch as spherical aberration and coma can be well corrected again with afewer lenses. With the above arrangement that allows the lens system tobe set up with a fewer lenses, size reductions and cost savings are thusachievable. Still, there is difficulty in reconciling the reduction inthe whole length of the lens system with slimming down each lens, aspreviously detailed with reference to the first zoom optical system.

However, if that positive lens is formed as a one-piece molded lens, itis then unnecessary to form it larger than the necessary outer diameter.The satisfaction of condition (3B) enables large power to be achievedwith a thin lens. In this way, further size reductions are achievable.

As the lower limit of 0.1 to condition (3B) is not reached, the powerbecomes too large relative to the principal point spacing. This does notonly result in an increased sensitivity to decentration, but also hasdifficulty in keeping the optical performance intact. As the upper limitof 6 is exceeded, the power becomes small relative to the principalpoint spacing and, hence, with one positive lens, it is difficult tohold back fluctuations of the above aberrations. In other words, aplurality of lenses must be used for obtaining good performance.

It is more preferable to satisfy the following condition (3B-2). In thiscase, good performance is obtainable with a reduced number of lenses.0.5<HH2/φ2<3  (3B-2)

It is even more preferable to satisfy the following condition (3B-3). Inthis case, it is easier to obtain good performance with a limited numberof lenses.1<HH2/φ2<1.5  (3B-3)

Preferably for the second zoom optical system, at least one one-piecelens in the second group should have at least one aspheric surface.

The advantage of, and the requirement for, the above arrangement is nowexplained. At the second group, light rays gain height. Therefore, if atleast one aspheric surface is introduced into the second group, it isthen possible to make effective correction for off-axis aberrations likeastigmatism and coma.

(3) Reference is now made to the type wherein the first group is anegative lens group, the second group is a positive lens group and thethird group is a positive lens group.

The third zoom optical system of the invention comprises, in order fromits object side, a first group having negative refracting power, asecond group having positive refracting power and a third group havingpositive refracting power, wherein at least one lens is formed bymolding of a first lens blank that provides a surface including at leastan optical function surface after molding and a second lens blank thatprovides a surface other than the surface including at least an opticalfunction surface after molding. In other words, at least one lenscomprises a one-piece lens wherein the first lens blank and the secondlens blank are integrated together.

The advantage of, and the requirement for, the above arrangement is nowexplained. A zoom optical system comprising, in order from its objectside, a lens group of negative refracting power, a lens group ofpositive refracting power and a lens group of positive refracting power,can be set up with a limited or reduced number of lenses, and so is bestsuited for size reductions and cost savings. With the one-piece lens,further size reductions are achievable. This is because for theone-piece lens any peripheral thickness for rounding is not required,when compared with the prior art lens processing, as previouslydescribed in conjunction with the first zoom optical system.

Such a one-piece lens is also so easy to handle that the cost for thefabrication of the zoom optical system can be cut short.

Here, with the third zoom optical system, zooming from its wide-angleend to its telephoto end, for instance, is at least carried out asdescribed just below. The first group moves in a concave locus towardthe object side, and the second group moves toward the object side.During zooming, the third group could move, too.

Preferably for the third zoom optical system, the one-piece lens shouldbe cemented to other lens.

Preferably for the third zoom optical system, the one-piece lens shouldbe an aspheric one-piece lens wherein at least one optical functionsurface is an aspheric surface.

Preferably for the third zoom optical system, the first group shouldcomprise at least one positive lens.

Preferably for the third zoom optical system, the first group shouldhave a negative lens located nearest to its object side.

Preferably for the third zoom optical system, the first group shouldcomprise at least one one-piece lens.

Preferably for the third zoom optical system, at least one of theone-piece lenses should have positive refracting power.

The advantages of, and the requirements for, the above arrangements arethe same as in the first zoom optical system.

Preferably for the third zoom optical system, at least one positive lensin the first group should satisfy the following condition.0.1<HH1/φ1<15  (2C)Here, HH1 is the principal point spacing (mm) of the positive lens inthe first group, and φ1 is the refracting power of the positive lens inthe first lens group.

The advantage of, and the requirement for, the above arrangement is thesame as already detailed in conjunction with the first zoom opticalsystem.

As the lower limit of 0.1 to condition (2C) is not reached, the powerbecomes too large relative to the principal point spacing. This does notonly result in an increased sensitivity to decentration, but also hasdifficulty in keeping the optical performance intact. As the upper limitof 15 is exceeded, the power becomes small relative to the principalpoint spacing. For this reason, chromatic aberration of magnification orother aberrations produced at the negative lens in the first groupremain undercorrected. Otherwise, a lot more lenses must be used forcorrection of chromatic aberration of magnification or the like.

It is more preferable to satisfy the following condition (2C-2). In thiscase, the optical system can be more slimmed down at the same low cost.0.5<HH1/φ1<7  (2C-2)

It is even more preferable to satisfy the following condition (2C-3). Inthis case, the optical system can be much more slimmed down at the samelow cost.1<HH1/φ1<4  (2C-3)

Preferably for the third zoom optical system, at least one one-piecelens in the first group should be cemented to other lens.

The advantage of, and the requirement for, the above arrangement is nowexplained. The incorporation of such a cemented lens in the first groupenables the sensitivity to decentration to be so diminished that theassembling of the optical system can be facilitated, leading to costsavings.

Preferably for the third zoom optical system, at least one one-piecelens in the first group should has at least one aspheric surface.

Preferably for the third zoom optical system, the second group shouldcomprise at least one negative lens.

Preferably for the third zoom optical system, the second group shouldhave a positive lens located nearest to its object side.

Preferably for the third zoom optical system, the second group shouldhave a negative lens located nearest to its image side.

Preferably for the third zoom optical system, the second group shouldcomprise at least one one-piece lens, wherein at least one of theone-piece lenses has positive refracting power.

The advantages of, and the requirements for, the above arrangements arethe same as described in conjunction with the first zoom optical system.

Preferably for the third zoom optical system, at least one positive lensin the second group should satisfy the following condition.0.1<HH2/φ2<10  (3C)Here, HH2 is the principal point spacing (mm) of the positive lens inthe second group, and φ2 is the refracting power of the positive lens inthe second group.

The advantage of, and the requirement for, the above arrangement is thesame as described with reference to the first zoom optical system.

As the lower limit of 0.1 to condition (3C) is not reached, the powerbecomes too large relative to the principal point spacing. This does notonly result in an increased sensitivity to decentration, but also hasdifficulty in keeping the optical performance intact. As the upper limitof 10 is exceeded, the power becomes small relative to the principalpoint spacing and, hence, the amount of movement of the second group cannever be reduced, resulting in an increase in the whole length of thelens system.

It is more preferable to satisfy the following condition (3C-2). In thiscase, the reduction in the whole length of the lens system can bereconciled with slimming down each lens.0.5<HH2/φ2<2  (3C-2)

It is even more preferable to satisfy the following condition (3C-3). Inthis case, it is easier to offer a sensible compromise between thereduction in the whole length of the lens system and slimming down eachlens.1<HH2/φ2<1.5  (3C-3)

Preferably for the third zoom optical system, at least one one-piecelens in the second group should has at least one aspheric surface.

The advantage of, and the requirement for, the above arrangement is nowexplained. A light beam incident on the first group having negativerefracting power travels through it, where the diameter of the lightbeam is enlarged. Thus, the light beam incident on the second group hasa large diameter. Therefore, if at least one aspheric surface isintroduced in the second group, fluctuations with zooming of variousaberrations such as spherical aberration and coma can be well correctedwith a more reduced number of lenses, so that the size and cost of theoptical system can be reduced.

Preferably for the third zoom optical system, the third group shouldcomprise at least one one-piece lens.

The advantage of, and the requirement for, the above arrangement is nowexplained. The lens in the third group, because of having a largeeffective area, increases in terms of the volume of the optical materialnecessary for it. Therefore, if the one-piece lens is used as the lensin the third group, the volume of that optical material can then bediminished with the result of cost savings. In addition, the one-piecelens is so easy to handle that the cost for the fabrication of the zoomoptical system can be cut short.

Preferably for the third zoom optical system, at least one of theone-piece lenses in the third group should be a positive lens havingpositive refracting power.

The advantage of, and the requirement for, the above arrangement is nowexplained. If the one-piece lens is used as the positive lens, the edgethickness difference of that positive lens can then be so diminishedthat the whole length of the lens system can be shortened. The positivelens in the third group increases in terms of the volume of the opticalmaterial necessary for it by reason of its large effective diameter.Therefore, if the one-piece lens is used as that positive lens, thevolume of that optical material becomes small so that cost savings areachievable.

Preferably for the third zoom optical system, at least one positive lensin the third group should satisfy the following condition.0.1<HH3/φ3<20  (4C)Here, HH3 is the principal point spacing (mm) of the positive lens inthe third group and φ3 is the refracting power of the positive lens inthe third group.

The advantage of, and the requirement for, the above arrangement is nowexplained. Increasing the power of the positive lens in the third groupmeans that the general power of the third group becomes strong.Increasing the power of the positive lens in the third group providesthe two following advantages: (1) at the wide-angle end, the exit pupilposition is spaced away from the image plane, so that it is easy toensure telecentric capability on the image side; and (2) the wholelength of the lens system can be shortened, because the range ofmovement of the third group along the optical axis for focusing purposescan become narrow, and the space between it and the second group remainsnarrow as well. Still, it is difficult to offer a sensible tradeoffbetween the reduction in the whole length of the lens system andslimming down each lens, as set forth with reference to the prior artlens processing regarding the first zoom optical system.

However, if that positive lens is formed as a one-piece molded lens, itis unnecessary to form it larger than the necessary outer diameter. Thesatisfaction of condition (4C) enables large power to be obtained with athin lens, so that further size reductions are achievable.

As the lower limit of 0.1 to condition (4C) is not reached, the powerbecomes too large relative to the principal point spacing. This does notonly result in an increased sensitivity to decentration, but also hasdifficulty in keeping the optical performance intact. As the upper limitof 20 is exceeded, the exit pupil position at the wide-angle end comesclose to the image plane, because the power becomes small relative tothe principal point spacing. As a result, it is impossible to ensuretelecentric capability on the image side.

It is more preferable to satisfy the following condition (4C-2). In thiscase, the reduction in the whole length of the lens system can be wellreconciled with slimming down each lens.0.5<HH3/φ3<8  (4C-2)

It is even more preferable to satisfy the following condition (4C-3). Inthis case, it is easier to reconcile the reduction in the whole lengthof the lens system with slimming down each lens.1<HH3/φ3<5  (4C-3)

Preferably for the third zoom optical system, at least one one-piecelens in the third group should has at least one aspheric surface.

The advantage of, and the requirement for, the above arrangement is nowexplained. Referring to the third zoom optical system, light rays at thethird group gains height at the telephoto end. Therefore, if at leastone aspheric surface is included in the third group, off-axisaberrations such as astigmatism, distortion and coma can then be wellcorrected with a more reduced number of lenses, so that the size andcost of the optical system can be reduced.

(4) Reference is made to the type wherein the first group is a negativelens group, the second group is a positive lens group, the third groupis a positive lens group and the fourth group is a negative lens group.

The fourth zoom optical system of the invention comprises, in order fromits object side, a first group having negative refracting power, asecond group having positive refracting power, a third group havingpositive refracting power and a fourth group having negative refractingpower, wherein at least one lens is formed by molding of a first lensblank that provides a surface including at least an optical functionsurface after molding and a second lens blank that provides a surfaceother than the surface including at least an optical function surfaceafter molding. In other words, at least one lens comprises a one-piecelens wherein the first lens blank and the second lens blank areintegrated together.

The advantage of, and the requirement for, the above arrangement is nowexplained. A zoom optical system comprising, in order from its objectside, a lens group of negative refracting power, a lens group ofpositive refracting power, a lens group of positive refracting power anda lens group of negative refracting power, can be set up with a limitedor reduced number of lenses, and so is best suited for size reductionsand cost savings. With the one-piece lens, further size reductions areachievable. This is because for the one-piece lens any peripheralthickness for rounding is not required, when compared with the prior artlens processing, as previously described in conjunction with the firstzoom optical system.

Such a one-piece lens is also so easy to handle that the fabricationcost of the zoom optical system can be cut short.

Here, with the fourth zoom optical system, zooming from its wide-angleend to its telephoto end, for instance, is at least carried out asdescribed just below. Upon zooming, the space between the first groupand the second group varies, and the space between the second group andthe third group varies. It is noted that zooming could be carried outwith a varying space between other lens groups and a varying spacebetween the fourth group and an image plane, and the third group couldbe used as a moving lens group for focusing.

Preferably for the fourth zoom optical system, the one-piece lens shouldbe cemented to other lens, or the one-piece lens should be an asphericone-piece lens wherein at least one optical function surface is anaspheric surface.

Preferably for the fourth zoom optical system, the first group shouldcomprise at least one positive lens.

Preferably for the fourth zoom optical system, the first group shouldhave a negative lens located nearest to its object side.

Preferably for the fourth zoom optical system, the first group shouldcomprise at least one one-piece lens.

Preferably for the fourth zoom optical system, at least one of theone-piece lenses should have positive refracting power.

The advantages of, and the requirements for, the above arrangements arethe same as in the first zoom optical system.

Preferably for the fourth zoom optical system, at least one positivelens in the first group should satisfy the following condition.0.1<HH1/φ1<10  (2D)Here, HH1 is the principal point spacing (mm) of the positive lens inthe first group, and φ1 is the refracting power of the positive lens inthe first group.

The advantage of, and the requirement for, the above arrangement is thesame as already set forth in conjunction with the first zoom opticalsystem.

As the lower limit of 0.1 to condition (2D) is not reached, the powerbecomes too large relative to the principal point spacing. This does notonly result in an increased sensitivity to decentration, but also hasdifficulty in keeping the optical performance intact. As the upper limitof 10 is exceeded, the power becomes small relative to the principalpoint spacing. For this reason, chromatic aberration of magnification orother aberrations produced at the negative lens in the first groupremain undercorrected. Otherwise, a lot more lenses must be used forcorrection of chromatic aberration of magnification or the like.

It is more preferable to satisfy the following condition (2D-2). In thiscase, the optical system can be more slimmed down at the same low cost.0.5<HH1/φ1<5  (2D-2)

It is even more preferable to satisfy the following condition (2D-3). Inthis case, the optical system can be much more slimmed down at the samelow cost.1<HH1/φ1<2.5  (2D-3)

Preferably for the fourth zoom optical system, at least one one-piecelens should be cemented to other lens.

The advantage of, and the requirement for, the above arrangement is thesame as in the third zoom optical system.

Preferably for the fourth zoom optical system, at least one one-piecelens in the first group should comprise at least one aspheric surface.

Preferably for the fourth zoom optical system, the second group shouldcomprise at least one negative lens.

Preferably for the fourth zoom optical system, the second group shouldhave a positive lens located nearest to its object side.

Preferably for the fourth zoom optical system, the second group shouldhave a negative lens located nearest to its image side.

Preferably for the fourth zoom optical system, the second group shouldcomprise at least one one-piece lens, wherein at least one of theone-piece lenses has positive refracting power.

The advantages of, and the requirements for, the above arrangements arethe same as described in conjunction with the first zoom optical system.

Preferably for the fourth zoom optical system, at least one positivelens in the second group should satisfy the following condition.0.1<HH2/φ2<10  (3D)Here, HH2 is the principal point spacing (mm) of the positive lens inthe second group, and φ2 is the refracting power of the positive lens inthe second group.

The advantage of, and the requirement for, the above arrangement is thesame as described with reference to the first zoom optical system.

As the lower limit of 0.1 to condition (3D) is not reached, the powerbecomes too large relative to the principal point spacing. This does notonly result in an increased sensitivity to decentration, but also hasdifficulty in keeping the optical performance intact. As the upper limitof 10 is exceeded, the power becomes small relative to the principalpoint spacing and, hence, the amount of movement of the second group cannever be reduced, resulting in an increase in the whole length of thelens system.

It is more preferable to satisfy the following condition (3D-2). In thiscase, the reduction in the whole length of the lens system can bereconciled with slimming down each lens.0.5<HH2/φ2<5  (3D-2)

It is even more preferable to satisfy the following condition (3D-3). Inthis case, it is easier to offer a sensible compromise between thereduction in the whole length of the lens system and slimming down eachlens.1<HH2/φ2<3.5  (3D-3)

Preferably for the fourth zoom optical system, at least one one-piecelens in the second group should comprise at least one aspheric surface.

Preferably for the fourth zoom optical system, the third group shouldcomprise at least one one-piece lens.

Preferably for the fourth zoom optical system, at least one of theone-piece lenses in the third group should be a positive lens havingpositive refracting power.

The advantage of, and the requirement for, the above arrangement is thesame as in the third zoom optical system.

Preferably for the fourth zoom optical system, at least one positivelens in the third group should satisfy the following condition.0.1<HH3/φ3<20  (4D)Here, HH3 is the principal point spacing (mm) of the positive lens inthe third group and φ3 is the refracting power of the positive lens inthe third group.

The advantage of, and the requirement for, the above arrangement is thesame as in the third zoom optical system.

As the lower limit of 0.1 to condition (4D) is not reached, the powerbecomes too large relative to the principal point spacing. This does notonly result in an increased sensitivity to decentration, but also hasdifficulty in keeping the optical performance intact. As the upper limitof 20 is exceeded, the exit pupil position at the wide-angle end comesclose to the image plane, because the power becomes small relative tothe principal point spacing. As a result, it is impossible to ensuretelecentric capability on the image side.

It is more preferable to satisfy the following condition (4D-2). In thiscase, the reduction in the whole length of the lens system can be wellreconciled with slimming down each lens.0.5<HH3/φ3<9  (4D-2)

It is even more preferable to satisfy the following condition (4D-3). Inthis case, it is easier to reconcile the reduction in the whole lengthof the lens system with slimming down each lens.1<HH3/φ3<4  (4D-3)

Preferably for the fourth zoom optical system, at least one one-piecelens in the third group should comprise at least one aspheric surface.

The advantage of, and the requirement for, the above arrangement is nowexplained. Referring to the fourth zoom optical system, at thewide-angle end, the diameter of a light beam through the third group islarge. Therefore, if at least one aspheric surface is introduced in thethird group, fluctuations with zooming of various aberrations such asspherical aberration and coma can then be well corrected with a morereduced number of lenses, resulting in size reductions and cost savingsof the optical system.

Preferably for the fourth zoom optical system, a one-piece lens shouldbe used in the fourth group (or the fourth group should comprise atleast one one-piece lens).

The advantage of, and the requirement for, the above arrangement is nowexplained. The volume of the optical material necessary for the lens inthe fourth group becomes large because of its large effective diameter.Therefore, if a one-piece lens is used as that lens in the fourth group,the volume of that optical material then becomes small, resulting incost savings. The one-piece lens is also so easy to handle that thefabrication cost of the zoom optical system can be cut short.

Preferably for the fourth zoom optical system, at lest one one-piecelens in the fourth group should comprise at least one aspheric surface.

The advantage of, and the requirement for, the above arrangement is nowexplained. At the fourth group, light rays gain height. Therefore, if atleast one aspheric surface is introduced in the fourth group, off-axisaberrations such as distortion and astigmatism can then be wellcorrected with a more reduced number of lenses, resulting in sizereductions and cost savings of the optical system.

(5) Reference is made to the type wherein the first group is a negativelens group, the second group is a positive lens group, the third groupis a negative lens group and the fourth group is a positive lens group.

The fifth zoom optical system of the invention comprises, in order fromits object side, a first group having negative refracting power, asecond group having positive refracting power, a third group havingnegative refracting power and a fourth group having positive refractingpower, wherein at least one lens is formed by molding of a first lensblank that provides a surface including at least an optical functionsurface after molding and a second lens blank that provides a surfaceother than the surface including at least an optical function surfaceafter molding. In other words, at least one lens comprises a one-piecelens wherein the first lens blank and the second lens blank areintegrated together.

The advantage of, and the requirement for, the above arrangement is nowexplained. A zoom optical system comprising, in order from its objectside, a lens group of negative refracting power, a lens group ofpositive refracting power, a lens group of negative refracting power anda lens group of positive refracting power, can be set up with a limitedor reduced number of lenses, and so is best suited for size reductionsand cost savings. With the one-piece lens, further size reductions areachievable. This is because for the one-piece lens any peripheralthickness for rounding is not required, when compared with the prior artlens processing, as previously described in conjunction with the firstzoom optical system.

Such a one-piece lens is also so easy to handle that the fabricationcost of the zoom optical system can be cut short.

Here, with the fifth zoom optical system, zooming from its wide-angleend to its telephoto end, for instance, is carried out as described justbelow. Upon zooming, the second group and the third group move towardthe object side in an independent fashion. It is understood that uponzooming, the first group or the first group, too, could move.

Preferably for the fifth zoom optical system, the one-piece lens shouldbe cemented to other lens, and the one-piece lens should be an asphericone-piece lens wherein at least one optical function surface is anaspheric surface.

Preferably for the fifth zoom optical system, the first group shouldcomprise at least one positive lens.

Preferably for the fifth zoom optical system, the first group shouldhave a negative lens located nearest to its object side.

Preferably for the fifth zoom optical system, the first group shouldcomprise at least one one-piece lens.

Preferably for the fifth zoom optical system, at least one of theone-piece lenses should have positive refracting power.

The advantages of, and the requirements for, the above arrangements arethe same as in the first zoom optical system.

Preferably for the fifth zoom optical system, at least one positive lensin the first group should satisfy the following condition.b 0.1<HH1/φ1<10  (2E)Here, HH1 is the principal point spacing (mm) of the positive lens inthe first group, and φ1 is the refracting power of the positive lens inthe first group.

The advantage of, and the requirement for, the above arrangement is thesame as already set forth in conjunction with the first zoom opticalsystem.

As the lower limit of 0.1 to condition (2E) is not reached, the powerbecomes too large relative to the principal point spacing. This does notonly result in an increased sensitivity to decentration, but also hasdifficulty in keeping the optical performance intact. As the upper limitof 10 is exceeded, the power becomes small relative to the principalpoint spacing. For this reason, chromatic aberration of magnification orother aberrations produced at the negative lens in the first groupremain undercorrected. Otherwise, a lot more lenses must be used forcorrection of chromatic aberration of magnification or the like.

It is more preferable to satisfy the following condition (2E-2). In thiscase, the optical system can be more slimmed down at the same low cost.0.5<HH1/φ1<6  (2E-2)

It is even more preferable to satisfy the following condition (2E-3). Inthis case, the optical system can be much more slimmed down at the samelow cost.1<HH1/φ1<4  (2E-3)

Preferably for the fifth zoom optical system, at least one one-piecelens in the first group should be cemented to other lens.

The advantage of, and the requirement for, the above arrangement is thesame as in the third zoom optical system.

Preferably for the fifth zoom optical system, at least one one-piecelens in the first group should comprise at least one aspheric surface.

The advantage of, and the requirement for, the above arrangement is thesame as in the first zoom optical system.

Preferably for the fifth zoom optical system, the second group shouldcomprise at least one negative lens.

The advantage of, and the requirement for, the above arrangement is nowexplained. The second group, because of having positive power, comprisesat least one positive lens. Therefore, if the negative lens isintroduced in the second group, fluctuations of chromatic aberration ofmagnification or the like with zooming can then be held back.

Preferably for the fifth zoom optical system, the second group shouldhave a positive lens located nearest to its object side.

Preferably for the fifth zoom optical system, the second group shouldhave a negative lens located nearest to its image side.

Preferably for the fifth zoom optical system, the second group shouldcomprise at least one one-piece lens, wherein at least one of theone-piece lenses has positive refracting power.

The advantages of, and the requirements for, the above arrangements arethe same as described in conjunction with the first zoom optical system.

Preferably for the fifth zoom optical system, at least one positive lensin the second group should satisfy the following condition.0.1<HH2/φ2<6  (3E)Here, HH2 is the principal point spacing (mm) of the positive lens inthe second group, and φ2 is the refracting power of the positive lens inthe second group.

The advantage of, and the requirement for, the above arrangement is thesame as described with reference to the first zoom optical system.

As the lower limit of 0.1 to condition (3E) is not reached, the powerbecomes too large relative to the principal point spacing. This does notonly result in an increased sensitivity to decentration, but also hasdifficulty in keeping the optical performance intact. As the upper limitof 6 is exceeded, the power becomes small relative to the principalpoint spacing and, hence, the amount of movement of the second group cannever be reduced, resulting in an increase in the whole length of thelens system.

It is more preferable to satisfy the following condition (3E-2). In thiscase, the reduction in the whole length of the lens system can bereconciled with slimming down each lens.0.5<HH2/φ2<3  (3E-2)

It is even more preferable to satisfy the following condition (3E-3). Inthis case, it is easier to offer a sensible compromise between thereduction in the whole length of the lens system and slimming down eachlens.1<HH2/φ2<2  (3E-3)

Preferably for the fifth zoom optical system, at least one one-piecelens in the second lens group should be cemented to other lens.

The advantage of, and the requirement for, the above arrangement is thesame as described with reference to the first zoom optical system.

Preferably for the fifth zoom optical system, at least one one-piecelens in the second group should comprise at least one aspheric surface.

As a light beam is incident on the first group having negativerefracting power, its diameter grows large. Therefore, if at least oneaspheric surface is introduced in the second group, fluctuations ofvarious aberrations can then be well corrected, resulting in theachievement of size reductions and cost savings. To decrease lensdiameter, the power of each lens must be increased. As the positivepower of the second group increases, however, there are significantchanges in the transverse magnification and aberrations of the secondgroup with zooming. Therefore, the second group should preferablyinclude an aspheric surface for the purposes of making correction foraberrations produced at the second group and held back aberrationfluctuations with zooming.

Preferably for the fifth zoom optical system, the third group shouldcomprise at least one one-piece lens.

The advantage of, and the requirement for, the above arrangement is nowexplained. As previously stated, the one-piece lens is so easy to handlethat the fabrication cost of the zoom optical system can be cut short.

Preferably for the fifth zoom optical system, the fourth group shouldcomprise at least one one-piece lens.

The advantage of, and the requirement for, the above arrangement is thesame as set forth with reference to the fourth zoom optical system.

Preferably for the fifth zoom optical system, at least one of theone-piece lenses in the fourth group should be a positive lens havingpositive refracting power.

The advantage of, and the requirement for, the above arrangement is nowexplained. If the one-piece lens is used as the positive lens, the edgethickness difference of that positive lens can then be diminished,resulting in a decrease in the whole length of the lens system.

The volume of the optical material necessary for the lens in the fourthgroup grows large because of its large effective diameter. Therefore, ifthe one-piece lens is used as the lens in the fourth group, the volumeof that optical material can then be decreased, resulting in costsavings. The one-piece lens is also so easy to handle that thefabrication cost of the zoom optical system can be cut short.

Preferably for the fifth zoom optical system, at least one positive lensin the fourth group should satisfy the following condition.0.1<HH4/φ4<10  (5E)Here, HH4 is the principal point spacing (mm) of the positive lens inthe fourth group and φ4 is the refracting power of the positive lens inthe fourth group.

The advantage of, and the requirement for, the above arrangement is nowexplained.

The advantage of, and the requirement for, the above arrangement is nowexplained. Increasing the power of the positive lens in the fourth groupmeans that the general power of the third group becomes strong,resulting in a reduction in the whole length of the lens system.Increasing the power of the positive lens in the fourth group providesthe following advantage: at the wide-angle end, the exit pupil positionis spaced away from the image plane, so that it is easy to ensuretelecentric capability on the image side. With the prior art lensprocessing, it is still difficult to offer a sensible tradeoff betweenthe reduction in the whole length of the lens system and slimming downeach lens, as set forth with reference to the prior art lens processingregarding the first zoom optical system.

However, if that positive lens is formed as a one-piece molded lens, itis unnecessary to form it larger than the necessary outer diameter. Thesatisfaction of condition (5E) enables large power to be obtained with athin lens, so that further size reductions are achievable.

As the lower limit of 0.1 to condition (5E) is not reached, the powerbecomes too large relative to the principal point spacing. This does notonly result in an increased sensitivity to decentration, but also hasdifficulty in keeping the optical performance intact. Exceeding theupper limit of 10 is not preferable, because the power becomes smallrelative to the principal point spacing, and so the exit pupil positionat the wide-angle end comes close to the image plane. As a result, it isimpossible to ensure telecentric capability on the image side.

It is more preferable to satisfy the following condition (5E-2). In thiscase, the reduction in the whole length of the lens system and theachievement of telecentric capability on the image side can be wellreconciled with slimming down each lens.0.5<HH4/φ4<7  (5E-2)

It is even more preferable to satisfy the following condition (5E-3). Inthis case, it is easier to reconcile the reduction in the whole lengthof the lens system and the achievement of telecentric capability on theimage side with slimming down each lens.1<HH4/φ4<5  (5E-3)

(6) Reference is made to the type wherein the first group is a negativelens group, the second group is a positive lens group, the third groupis a positive lens group and the fourth group is a positive lens group.

The sixth zoom optical system of the invention comprises, in order fromits object side, a first group having negative refracting power, asecond group having positive refracting power, a third group havingpositive refracting power and a fourth group having positive refractingpower, wherein at least one lens is formed by molding of a first lensblank that provides a surface including at least an optical functionsurface after molding and a second lens blank that provides a surfaceother than the surface including at least an optical function surfaceafter molding. In other words, at least one lens comprises a one-piecelens wherein the first lens blank and the second lens blank areintegrated together.

The advantage of, and the requirement for, the above arrangement is nowexplained. A zoom optical system comprising, in order from its objectside, a lens group of negative refracting power, a lens group ofpositive refracting power, a lens group of positive refracting power anda lens group of positive refracting power, can be set up with a limitedor reduced number of lenses, and so is best suited for size reductionsand cost savings. With the one-piece lens, further size reductions areachievable. This is because for the one-piece lens any peripheralthickness for rounding is not required, when compared with the prior artlens processing, as previously described in conjunction with the priorart lens processing regarding the first zoom optical system.

Such a one-piece lens is also so easy to handle that the fabricationcost of the zoom optical system can be cut short.

Here, with the sixth zoom optical system, zooming from its wide-angleend to its telephoto end, for instance, is at least carried out asfollows. Upon zooming, the first group moves in a concave locus towardthe object side, and the second lens group moves toward the object side.It is understood that upon zooming, the third group and the fourthgroups could move.

Preferably for the sixth zoom optical system, the one-piece lens shouldbe cemented to other lens.

Preferably for the sixth zoom optical system, the one-piece lens shouldbe an aspheric one-piece lens wherein at least one optical functionsurface is an aspheric surface.

Preferably for the sixth zoom optical system, the first group shouldcomprise at least one positive lens.

Preferably for the sixth zoom optical system, the first group shouldhave a negative lens located nearest to its object side.

Preferably for the sixth zoom optical system, the first group shouldcomprise at least one one-piece lens.

Preferably for the sixth zoom optical system, at least one of theone-piece lenses should have positive refracting power.

The advantages of, and the requirements for, the above arrangements arethe same as in the first zoom optical system.

Preferably for the sixth zoom optical system, at least one positive lensin the first group should satisfy the following condition.0.1<HH1/φ1<15  (2F)Here, HH1 is the principal point spacing (mm) of the positive lens inthe first group, and φ1 is the refracting power of the positive lens inthe first group.

The advantage of, and the requirement for, the above arrangement is thesame as already set forth in conjunction with the first zoom opticalsystem.

As the lower limit of 0.1 to condition (2F) is not reached, the powerbecomes too large relative to the principal point spacing. This does notonly result in an increased sensitivity to decentration, but also hasdifficulty in keeping the optical performance intact. As the upper limitof 15 is exceeded, the power becomes small relative to the principalpoint spacing. For this reason, chromatic aberration of magnification orother aberrations produced at the negative lens in the first groupremain undercorrected. Otherwise, a lot more lenses must be used forcorrection of chromatic aberration of magnification or the like.

It is more preferable to satisfy the following condition (2F-2). In thiscase, the optical system can be more slimmed down at the same low cost.0.5<HH1/φ1<7  (2F-2)

It is even more preferable to satisfy the following condition (2F-3). Inthis case, the optical system can be much more slimmed down at the samelow cost.1<HH1/φ1<4  (2F-3)

Preferably for the sixth zoom optical system, at least one one-piecelens in the first group should be cemented to other lens.

The advantage of, and the requirement for, the above arrangement is thesame as in the third zoom optical system.

Preferably for the sixth zoom optical system, at least one one-piecelens in the first group should have at least one aspheric surface.

The advantage of, and the requirement for, the above arrangement is nowexplained. Referring to the sixth zoom optical system, at the wide-angleend, the diameter of a light beam through the third group is large.Therefore, if at least one aspheric surface is introduced in the thirdgroup, fluctuations with zooming of various aberrations such asspherical aberration and coma can then be well corrected with a morereduced number of lenses, resulting in size reductions and cost savingsof the optical system.

At the telephoto end, on the other hand, the diameter of a light beamthrough the first group grows large. Therefore, if at least one asphericsurface is introduced in the third group, fluctuations with zooming ofvarious aberrations such as spherical aberration and coma can then bewell corrected with a more reduced number of lenses, again resulting insize reductions and cost savings of the optical system.

Preferably for the sixth zoom optical system, the second group shouldcomprise at least one negative lens.

Preferably for the sixth zoom optical system, the second group shouldhave a positive lens located nearest to its object side.

Preferably for the sixth zoom optical system, the second group shouldhave a negative lens located nearest to its image side.

Preferably for the fifth zoom optical system, the second group shouldcomprise at least one one-piece lens, wherein at least one of theone-piece lenses has positive refracting power.

The advantages of, and the requirements for, the above arrangements arethe same as described in conjunction with the first zoom optical system.

Preferably for the sixth zoom optical system, at least one positive lensin the second group should satisfy the following condition.0.1<HH2/φ2<10  (3F)Here, HH2 is the principal point spacing (mm) of the positive lens inthe second group, and φ2 is the refracting power of the positive lens inthe second group.

The advantage of, and the requirement for, the above arrangement is thesame as described with reference to the first zoom optical system.

As the lower limit of 0.1 to condition (3F) is not reached, the powerbecomes too large relative to the principal point spacing. This does notonly result in an increased sensitivity to decentration, but also hasdifficulty in keeping the optical performance intact. As the upper limitof 10 is exceeded, the power becomes small relative to the principalpoint spacing and, hence, the amount of movement of the second group cannever be reduced, resulting in an increase in the whole length of thelens system.

It is more preferable to satisfy the following condition (3F-2). In thiscase, the reduction in the whole length of the lens system can bereconciled with slimming down each lens.0.5<HH2/φ2<2  (3F-2)

It is even more preferable to satisfy the following condition (3F-3). Inthis case, it is easier to offer a sensible compromise between thereduction in the whole length of the lens system and slimming down eachlens.1<HH2/φ2<1.5  (3F-3)

Preferably for the sixth zoom optical system, at least one one-piecelens in the second group should have at least one aspheric surface.

Preferably for the sixth zoom optical system, the third group shouldcomprise at least one one-piece lens.

Preferably for the sixth zoom optical system, at least one of theone-piece lenses in the third group should be a positive lens havingpositive refracting power.

Preferably for the sixth zoom optical system, at least one positive lensin the third group should satisfy the following condition.0.1<HH3/φ3<20  (4F)Here, HH3 is the principal point spacing (mm) of the positive lens inthe third group and φ3 is the refracting power of the positive lens inthe third group.

The advantage of, and the requirement for, the above arrangement is thesame as set forth with reference to the third zoom optical system.

As the lower limit of 0.1 to condition (4F) is not reached, the powerbecomes too large relative to the principal point spacing. This does notonly result in an increased sensitivity to decentration, but also hasdifficulty in keeping the optical performance intact. Exceeding theupper limit of 20 is not preferable, because the power becomes smallrelative to the principal point spacing, and so the exit pupil positionat the wide-angle end comes close to the image plane. As a result, it isimpossible to ensure telecentric capability on the image side.

It is more preferable to satisfy the following condition (4F-2). In thiscase, the reduction in the whole length of the lens system can bereconciled with slimming down each lens.0.5<HH3/φ3<8  (4F-2)

It is even more preferable to satisfy the following condition (4F-3). Inthis case, it is easier to reconcile the reduction in the whole lengthof the lens system with slimming down each lens.1<HH3/φ3<5  (4F-3)

Preferably for the sixth zoom optical system, at least one one-piecelens in the third group should have at least one aspheric surface.

Preferably for the sixth zoom optical system, the fourth group shouldcomprise at least one one-piece lens.

The advantages of, and the requirements for, the above arrangements arethe same as set fourth in conjunction with the fourth zoom opticalsystem.

Preferable for the sixth zoom optical system, the at least one of theone-piece lenses should have positive refracting power.

The advantage of, and the requirement for, the above arrangement is thesame as set forth in connection with the fifth zoom optical system.

Preferably for the sixth zoom optical system, at least one positive lensin the fourth group should satisfy the following condition.0.1<HH4/φ4<20  (5F)Here, HH4 is the principal point spacing (mm) of the positive lens inthe fourth group and φ3 is the refracting power of the positive lens inthe fourth group.

The advantage of, and the requirement for, the above arrangement is thesame as set forth with reference to the fifth zoom optical system.

As the lower limit of 0.1 to condition (5F) is not reached, the powerbecomes too large relative to the principal point spacing. This does notonly result in an increased sensitivity to decentration, but also hasdifficulty in keeping the optical performance intact. As the upper limitof 20 is exceeded, the power becomes small relative to the principalpoint spacing, and so the exit pupil position at the wide-angle endcomes close to the image plane. As a result, it is impossible to ensuretelecentric capability on the image side.

It is more preferable to satisfy the following condition (5F-2). In thiscase, the reduction in the whole length of the lens system and thetelecentric capability on the image side can be reconciled with slimmingdown each lens.0.5<HH4/φ4<8  (5F-2)

It is even more preferable to satisfy the following condition (5F-3). Inthis case, it is easier to reconcile the reduction in the whole lengthof the lens system and the telecentric capability on the image side withslimming down each lens.1<HH4/φ4<5  (5F-3)

Preferably for the sixth zoom optical system, at least one one-piecelens in the third group should have at least one aspheric surface.

The advantage of, and the requirement for, the above arrangement is nowexplained. At the wide-angle end, the diameter of a light beam throughthe fourth group becomes large. Therefore, if at least one asphericsurface is included in the fourth group, fluctuations with zooming ofvarious aberrations such as spherical aberration and coma can then bewell corrected with a reduced number of lenses. This is preferable tosize reductions and cost savings.

(7) Reference is made to the type wherein the first group is a positivelens group, the second group is a negative lens group, the third groupis a positive lens group and the fourth group is a positive lens group.

The seventh zoom optical system of the invention comprises, in orderfrom its object side, a first group having positive refracting power, asecond group having negative refracting power, a third group havingpositive refracting power and a fourth group having positive refractingpower, wherein at least one lens is formed by molding of a first lensblank that provides a surface including at least an optical functionsurface after molding and a second lens blank that provides a surfaceother than the surface including at least an optical function surfaceafter molding. In other words, at least one lens comprises a one-piecelens wherein the first lens blank and the second lens blank areintegrated together.

The advantage of, and the requirement for, the above arrangement is nowexplained. A zoom optical system comprising, in order from its objectside, a lens group of positive refracting power, a lens group ofnegative refracting power, a lens group of positive refracting power anda lens group of positive refracting power, can be set up with a limitedor reduced number of lenses, providing an optical system of highperformance and having a fixed total length, and so is best suited forsize reductions and cost savings. With the one-piece lens, further sizereductions are achievable. This is because for the one-piece lens anyperipheral thickness for rounding is not required, when compared withthe prior art lens processing, as previously described in conjunctionwith the prior art lens processing regarding the first zoom opticalsystem.

Such a one-piece lens is also so easy to handle that the fabricationcost of the zoom optical system can be cut short.

Here, with the seventh zoom optical system, zooming from its wide-angleend to its telephoto end, for instance, is carried out as follows. Uponzooming, the second group moves toward the image side, and the thirdgroup and the fourth group moves toward the object side with their spacebecoming wide. It is understood that the first group, too, could moveduring zooming.

Preferably for the seventh zoom optical system, the one-piece lensshould be cemented to other lens. Preferably for the seventh zoomoptical system, the one-piece lens should be an aspheric one-piece lenswherein at least one optical function surface is an aspheric surface.

The advantages of, and the requirements for, the above arrangements arethe same as set forth in conjunction with the first zoom optical system.

Preferably for the seventh zoom optical system, the first group shouldcomprise at least one positive lens.

The advantage of, and the requirement for, the above arrangement is nowexplained. The lens in the first group, because of having a largeeffective diameter, grows large in terms of the necessary volume. Withone-piece lens used in the first lens group, however, the volume of theoptical system can be diminished. As a result, cost savings areachievable. The volume of the lens itself, too, becomes so small thatthe optical system can be slimmed down. The one-piece lens is also soeasy to handle that the fabrication cost of the optical system can becut short.

Preferably for the seventh zoom optical system, at least one of theone-piece lenses in the first group should have positive refractingpower.

The advantage of, and the requirement for, the above arrangement is nowexplained. For the positive lens in the first group, it is preferable touse a high-refractive-index, high-dispersion optical material so as tomake correction for chromatic aberration, spherical aberration, etc.Commonly, however, the high-refractive-index, high-dispersion opticalmaterial costs much. In addition, the positive lens in the first group,because of having a large effective diameter, grows large in terms ofthe necessary volume. However, it is preferable to use a one-piece lensas that positive lens, because the volume of such an optical materialcan be diminished, resulting in cost savings.

Also, the volume of the lens itself becomes so small that the opticalsystem can be slimmed down. The use of a one-piece lens as the positivelens ensures that the edge thickness difference of the positive lensbecomes small. Accordingly, the total length of the optical system canbe shortened.

Preferably for the seventh zoom optical system, at least one positivelens in the first group should satisfy the following condition.0.1<HH1/φ1<20  (2G)Here, HH1 is the principal point spacing (mm) of the positive lens inthe first group, and φ1 is the refracting power of the positive lens inthe first group.

The advantage of, and the requirement for, the above arrangement is nowexplained. As the positive lens in the first group is weak, it incurs anincrease in the total length of the lens system simultaneously with anincrease the diameter of the front lens. Thus, the positive lens in thefirst group should preferably have large power. With the conventionallens processing, however, it is difficult to offer a sensible tradeoffbetween cost savings and size reductions, as detailed in conjunctionwith the first zoom optical system.

However, if this positive lens is formed by molding as a one-piece lens,it is then unnecessary to form it larger than the necessary outerdiameter. The satisfaction of condition (2G) enables larger power to beachieved by a thin lens. Thus, cost savings and size reductions aresimultaneously achievable.

As the lower limit of 0.1 to condition (2G) is not reached, the powerbecomes too large relative to the principal point spacing. This does notonly result in an increased sensitivity to decentration, but also hasdifficulty in keeping the optical performance intact. As the upper limitof 20 is exceeded, the power becomes small relative to the principalpoint spacing. This does not only result in an increase in the totallength of the lens system, but also incurs an increase in the diameterof the front lens, rendering the size reductions of the optical systemdifficult.

It is more preferable to satisfy the following condition (2G-2) In thiscase, the optical system can be more slimmed down at the same low cost.0.5<HH1/φ1<10  (2G-2)

It is even more preferable to satisfy the following condition (2G-3). Inthis case, the optical system can be much more slimmed down at the samelow cost.1<HH1/φ1<5  (2G-3)

Preferably for the seventh zoom optical system, the second group shouldcomprise at least one positive lens.

The advantage of, and the requirement for, the above arrangement is nowexplained. The second group, because of having negative power, comprisesat least one negative lens. Therefore, if a positive lens is included inthe second group, fluctuations with zooming of various aberrations suchas spherical aberration and chromatic aberration of magnification canthen be held back.

Preferable for the seventh optical system, the second group should havea positive lens located nearest to its object side.

The advantage of, and the requirement for, the above arrangement is nowexplained. It is possible to reduce the effective diameters of thelenses in the second group and the whole length of the lens system.

Preferably for the seventh zoom optical system, the second group shouldcomprise at least one one-piece lens.

The advantage of, and the requirement for, the above arrangement is thesame as set forth in connection with the second zoom optical system.

Preferably for the seventh zoom optical system, at least one of theone-piece lenses in the second group should have positive refractingpower.

The second group, because of having negative power, comprises at leastone negative lens. Therefore, if a positive lens is included in thesecond group, fluctuations with zooming of various aberrations such asspherical aberration and chromatic aberration of magnification can thenbe held back.

For the positive lens in the second group, it is preferable to use ahigh-refractive-index, high-dispersion optical material so as to makecorrection for chromatic aberration, spherical aberration, etc.Commonly, however, the high-refractive-index, high-dispersion opticalmaterial costs much. In addition, the positive lens in the second group,because of having a large effective diameter, grows large in terms ofthe necessary volume. Therefore, it is preferable to use a one-piecelens as that positive lens, because the volume of such an opticalmaterial can be diminished, resulting in cost savings.

Also, the volume of the lens itself becomes so small that the opticalsystem can be slimmed down. The one-piece lens is also easy to handlethat the fabrication cost of the optical system can be cut short.

Preferably for the seventh zoom optical system, at least one positivelens in the second group should satisfy the following condition:0.1<HH2/φ2<15  (3G)Here, HH2 is the principal point spacing (mm) of the positive lens inthe second group, and φ2 is the refracting power of the positive lens inthe second lens group.

The advantage of, and the requirement for, the above arrangement is nowexplained. To reduce the effective diameters of the lenses and the wholelength of the lens system, it is preferable for the negative lens in thesecond group to have large power. To make good correction forfluctuations of spherical aberration, coma, etc. with zooming,therefore, it is preferable for the second group to comprise a positivelens of large power. With the prior art lens processing, however, thereis difficulty in balancing cost savings against size reductions, asdetailed in conjunction with the first zoom optical system.

However, if this positive lens is formed by molding as a one-piece lens,it is then unnecessary to form it larger than the necessary outerdiameter. The satisfaction of condition (3G) enables larger power to beachieved by a thin lens. Thus, cost savings and size reductions aresimultaneously achievable.

As the lower limit of 0.1 to condition (3G) is not reached, the powerbecomes too large relative to the principal point spacing. This does notonly result in an increased sensitivity to decentration, but also hasdifficulty in keeping the optical performance intact. As the upper limitof 15 is exceeded, the power becomes small relative to the principalpoint spacing. This has difficulty in holding back fluctuations withzooming of various aberrations such as spherical aberration and comaproduced at the negative lens in the second group. As a result, a lotmore lenses will be needed to obtain satisfactory performance.

It is more preferable to satisfy the following condition (3G-2). In thiscase, the reduction in the overall length of the lens system can bereconciled with slimming down each lens.0.5<HH2/φ2<7  (3G-2)

It is even more preferable to satisfy the following condition (3G-3). Inthis case, it is easier to reconcile the reduction in the overall lengthof the lens system with slimming down each lens.1<HH2/φ2<4  (3G-3)

Preferably for the sixth zoom optical system, at least one one-piecelens in the second group should be cemented to other lens.

The advantage of, and the requirement for, the above arrangement is thesame as in the third zoom optical system.

Preferably for the seventh zoom optical system, at least one one-piecelens in the second group should have at least one aspheric surface.

The advantage of, and the requirement for, the above arrangement is nowexplained. Referring to the seventh zoom optical system, at thewide-angle end, light rays through the second group gain height.Therefore, if at least one aspheric surface is introduced in the secondgroup, off-axis aberrations such as astigmatism, distortion, coma, etc.can then be well corrected with a more reduced number of lenses, leadingto size reductions and cost savings of the optical system.

At the telephoto end, on the other hand, the diameter of a light beamthrough the second group grows large. Therefore, if at least oneaspheric surface is introduced in the second group, sphericalaberration, coma and so on can then be well corrected with a morereduced number of lenses, again resulting in size reductions and costsavings of the optical system. Again, the optical system can be slimmeddown at low costs.

Preferably for the seventh zoom optical system, the third group shouldcomprise at least one negative lens.

The advantage of, and the requirement for, the above arrangement is nowexplained. The third group, because of having positive power, comprisesat least one positive lens. Therefore, if a negative lens is included init, fluctuations with zooming of various aberrations such as coma,astigmatism and longitudinal chromatic aberration can then be held back.

Preferably for the seventh zoom optical system, the third group shouldhave a positive lens located nearest to its object side.

The advantage of, and the requirement for, the above arrangement is nowexplained. By locating the positive lens nearest to the object side ofthe third group, the principal points are allowed to move toward thesecond group, so that the principal point spacing between the secondgroup and the third group can be shortened, leading to a reduction inthe whole length of the lens system.

Preferably for the seventh zoom optical system, the third group shouldcomprise at least one one-piece lens, wherein at least one of theone-piece lenses has positive refracting power.

The advantage of, and the requirement for, the above arrangement is nowexplained. By using a one-piece lens as the positive lens, the edgethickness difference of the positive lens can be made so small that thewhole length of the lens system can be shortened.

Preferably for the positive lens in the third group, it is preferable touse a high-refractive-index, low-dispersion optical material so as tohold back longitudinal chromatic aberration, spherical aberration,astigmatism, etc. Commonly, however, the high-refractive-index,low-dispersion optical material costs much. Therefore, if the positivelens is provided as a one-piece lens, then the volume of the opticalmaterial can be made small, resulting in cost savings.

The volume of the lens itself becomes so small that the optical systemcan be slimmed down. The one-piece lens is also easy to handle that thefabrication cost of the optical system can be cut short.

Preferably for the seventh zoom optical system, at least one positivelens in the third group should satisfy the following condition.0.1<HH3/φ3<8  (4G)Here, HH3 is the principal point spacing (mm) of the positive lens inthe third group, and φ3 is the refracting power of the positive lens inthe third group.

The advantage of, and the requirement for, the above arrangement is nowexplained. By increasing the power of the positive lens located in thethird group, the distance of movement of the third group can beshortened. This also results in a decrease in the whole length of thelens system. With the conventional lens processing, however, there ismuch difficulty in balancing cost savings against size reductions, asdetailed in connection with the first zoom optical system.

However, if the positive lens is formed as a one-piece lens, it is thenunnecessary to form it larger than the necessary outer diameter. Thesatisfaction of condition (4G) enables large power to be achieved with athin lens and, hence, further size reductions to be obtained.

As the lower limit of 0.1 to condition (4G) is not reached, the powerbecomes too large relative to the principal point spacing. This does notonly result in an increased sensitivity to decentration, but also hasdifficulty in keeping the optical performance intact. As the upper limitof 8 is exceeded, the power becomes small relative to the principalpoint spacing and, hence, the amount of movement of the second group cannever be reduced, resulting in an increase in the whole length of thelens system.

It is more preferable to satisfy the following condition (4G-2). In thiscase, the reduction in the whole length of the lens system can bereconciled with slimming down each lens.0.5<HH3/φ3<5  (4G-2)

It is even more preferable to satisfy the following condition (4G-3). Inthis case, it is easier to offer a sensible compromise between thereduction in the whole length of the lens system and slimming down eachlens.1<HH3/φ3<2.5  (4G-3)

Preferably for the seventh zoom optical system, at least one one-piecelens in the third group should have at least one aspheric surface.

The advantage of, and the requirement for, the above arrangement is nowexplained. In the seventh optical system, the diameter of a light beamis enlarged by the second group having negative refracting power, and soat the wide-angle end, the diameter of a light beam through the thirdgroup becomes large. With this in mind, at least one aspheric surface isintroduced in the third group. As a result, fluctuations with zooming ofvarious aberrations such as spherical aberration and coma can be wellcorrected with a more reduced number of lenses. Therefore, the opticalsystem can be slimmed down at low cost.

Preferably for the seventh zoom optical system, the fourth group shouldcomprise at least one one-piece lens.

The advantage of, and the requirement for, the above arrangement is thesame as in the fourth zoom optical system.

Preferably for the seventh zoom optical system, at least one of theone-piece lenses in the fourth group should be a positive lens havingpositive refracting power.

The advantage of, and the requirement for, the above arrangement is thesame as in the fifth zoom optical system.

Preferably for the seventh zoom optical system, at least one positivelens in the fourth group should satisfy the following condition.0.1<HH4/φ4<10  (5G)Here, HH4 is the principal point spacing (mm) of the positive lens inthe fourth group and φ4 is the refracting power of the positive lens inthe fourth group.

The advantage of, and the requirement for, the above arrangement is thesame as set forth with reference to the fifth zoom optical system.

As the lower limit of 0.1 to condition (5G) is not reached, the powerbecomes too large relative to the principal point spacing. This does notonly result in an increased sensitivity to decentration, but also hasdifficulty in keeping the optical performance intact. Exceeding theupper limit of 10 is not preferable, because the power becomes smallrelative to the principal point spacing, and so the exit pupil positionat the wide-angle end comes close to the image plane. As a result, it isimpossible to ensure telecentric capability on the image side.

It is more preferable to satisfy the following condition (5G-2). In thiscase, the reduction in the whole length of the lens system and thetelecentric capability on the image side can be reconciled with slimmingdown each lens.0.5<HH4/φ4<7  (5G-2)

It is even more preferable to satisfy the following condition (5G-3). Inthis case, it is easier to reconcile the reduction in the whole lengthof the lens system and telecentric capability on the image side withslimming down each lens.1<HH4/φ4<4  (5G-3)

Preferably for the seventh zoom optical system, at least one one-piecelens in the fourth group should have at least one aspheric surface.

The advantage of, and the requirement for, the above arrangement is nowexplained. At the wide-angle end, light rays through the fourth groupgain height. Therefore, if at least one aspheric surface is included inthe fourth group, off-axis aberrations such as distortion andastigmatism can then be well corrected with a more reduced number oflenses. As a result, the optical system can be slimmed down at low cost.

Preferably, the electronic system of the invention should comprise anyone of the zoom optical systems as described above, and an electronicimage pickup device located on an image side thereof.

The above zoom optical systems are each of smaller size and lower costthan ever before. Therefore, if any one of them is mounted in the formof an imaging optical system on an electronic system, the size and costof the electronic system can then be much more reduced. It is noted thatthe electronic system intended herein includes digital cameras, videocameras, digital video units, personal computers, mobile computers,cellar phone, personal digital assistants, etc.

Examples under the categories of the 1^(st) to 7^(th) zoom opticalsystems (zoom lenses) are now explained with reference to theaccompanying drawings. For instance, Example 1 of the first zoom opticalsystem is designated as “Example 1-1”, and Example 2 of the fifth zoomoptical system as “Example 5-2”. Lens section diagrams and aberrationdiagrams for each lens are provided. Each lens section diagram is takenalong the optical axis of each zoom optical system at the wide-angle end(a), in an intermediate setting (b) and the telephoto end (c) uponfocusing on an infinite object point. Throughout the drawings, G1 is thefirst lens group; G2 is the second lens group; G3 is the third lensgroup; G4 is the fourth lens group; S is an aperture stop; F isplane-parallel plate group such as a near infrared cut filter, alow-pass filter and a cover glass for the electronic image pickupdevice; and I is an image plane. The aberration diagrams are providedfor spherical aberration, astigmatism, chromatic aberration ofmagnification and distortion at the wide-angle end (a), in theintermediate setting (b) and at the telephoto end (c) upon focusing onan infinite object point. In these aberration diagrams, “FIY” stands foran image height.

-   (1) Zoom optical system wherein the first group is a negative lens    group and the second group is a positive lens group

Examples 1-1 and 1-2 of the first zoom optical system (zoom lens) arenow explained with reference to the drawings. FIGS. 7 and 8 areillustrative in lens section along the optical axes of Examples 1-1 and1-2 at the wide-angle ends (a), in intermediate settings (b) and at thetelephoto ends (c), respectively, upon focusing on an infinite objectpoint. FIGS. 9 and 10 are aberration diagrams for spherical aberration,astigmatism and chromatic aberration of magnification of Examples 1-1and 1-2 at the wide-angle ends (a), in the intermediate settings (b) andat the telephoto ends (c), respectively, upon focusing on an infiniteobject point.

EXAMPLE 1-1

FIG. 7 is illustrative in section of the zoom optical system of Example1-1, which is made up of, in order from its object side, a first lensgroup G1 an aperture stop S and a second lens group G2. Upon zoomingfrom the wide-angle end to the telephoto end of the optical system, thefirst lens group G1 moves in a concave locus toward the object side andis located in the same position at the telephoto end as at thewide-angle end, and the second lens group G2 moves in unison with theaperture stop S toward the object side.

The first lens group G1 has generally negative power, and is composedof, in order from its object side, a double-concave negative lens and adoublet consisting of a double-convex positive lens and a double-concavenegative lens. Two aspheric surfaces are used at both surfaces of thedouble-concave negative lens.

The second lens group G2 has generally positive power, and is composedof, in order from its object side, a double-convex positive lens and adoublet consisting of a double-convex positive lens and a double-concavenegative lens. Two aspheric surfaces are applied: one at the surfacenearest to the object side and another at the surface nearest to theimage side of the second lens group G2.

The lenses that form the zoom optical system of this example are allone-piece lenses except the double-concave negative lens on the imageside of the second lens group G2. Each one-piece lens has beenfabricated by the process shown in FIG. 1.

One exemplary one-piece lens 10 is shown in FIG. 11. This one-piece lensis used on the zoom optical system of this example. FIG. 11 is asectional view of the doublet in the second lens group G2, wherein adouble-convex positive lens on the object side is integrated with thedoublet into the one-piece lens 10, and a double-concave negative lensis cemented to its image side. The second lens blank 12 has a thicknessof 0.3 mm. Although not shown in FIG. 11, the second lens blank 12 couldbe processed simultaneously with the formation of a hole or an irregularpattern.

EXAMPLE 1-2

FIG. 8 is illustrative in section of the zoom optical system of Example1-2, which is made up of, in order from its object side, a first lensgroup G1, an aperture stop S and a second lens group G2. Upon zoomingfrom the wide-angle end to the telephoto end of the optical system, thefirst lens group G1 moves in a concave locus toward the object side ofthe optical system and is located in much the same position at thetelephoto end as at the wide-angle end, and the second lens group G2moves in unison with the aperture stop S toward the object side.

The first lens group has generally negative power, and is composed of,in order from its object side, a double-concave negative lens and apositive meniscus lens concave on its object side. One aspheric surfaceis applied to the object-side surface of the double-concave negativelens.

The second lens group G2 has generally positive power, and is composedof, in order from its object side, a doublet consisting of adouble-convex positive lens and a negative meniscus lens convex on itsobject side and a negative meniscus lens convex on its image side. Twoaspheric surfaces are used: one at the surface nearest to the objectside and another at the surface nearest to the image side of the secondlens group G2.

The lenses that form the zoom optical system of this example are allone-piece lenses except the negative meniscus lens on the object side ofthe second lens group G2. Each one-piece lens has been fabricated by theprocess shown in FIG. 3.

One exemplary one-piece lens 10 used herein is shown in FIGS. 12 and 13.FIG. 12 is illustrative in section of the doublet in the second lensgroup G2. In this doublet, the object-side double-convex positive lensis formed as the one-piece lens 10 with the negative meniscus lenscemented to the image side thereof. The second lens blank 12 is 0.25 mmin thickness. FIG. 13 is illustrative in section of the image-side lensin the second lens group G2. In this lens, the negative meniscus lens isformed as the one-piece lens 10. The second lens blank 12 is 1.5 mm inthickness. Although not shown in FIGS. 12 and 13, the second lens blank12 could be processed simultaneously with the provision of a hole or anirregular pattern (see FIG. 3).

Numerical data on each of the above examples will be enumerated later.

-   (2) Zoom optical system wherein the first group is a positive lens    group and the second group is a negative lens group

Examples 2-1 and 2-2 of the second zoom optical system (zoom lens) arenow explained with reference to the drawings. FIGS. 14 and 15 areillustrative in lens section along the optical axes of Examples 2-1 and2-2 at the wide-angle ends (a), in intermediate settings (b) and at thetelephoto ends (c), respectively, upon focusing on an infinite objectpoint. FIGS. 16 and 17 are aberration diagrams for spherical aberration,astigmatism and chromatic aberration of magnification of Examples 2-1and 2-2 at the wide-angle ends (a), in the intermediate settings (b) andat the telephoto ends (c), respectively, upon focusing on an infiniteobject point.

EXAMPLE 2-1

FIG. 14 is illustrative of the zoom optical system of Example 2-1, whichis made up of, in order from its object side, an aperture stop S, afirst lens group G1 and a second lens group G2. Upon zooming from thewide-angle end to the telephoto end of the optical system, the firstlens group G1 and the aperture stop S move in unison toward the objectside, and the second lens group G2 moves toward the object side with adecreasing space between it and the first lens group G1.

The first lens group G1 has generally positive power, and is composedof, in order from its object side, a positive meniscus lens concave onits object side, a negative meniscus lens convex on its object side anda double-convex positive lens. Two aspheric surfaces are applied to bothsurfaces of the positive meniscus lens, and one aspheric surface isapplied to the image-side surface of the double-convex positive lens.

The second lens group G2 has generally negative power, and is composedof, in order from its object side, a positive meniscus lens concave onits object side and a double-concave negative lens. One aspheric surfaceis applied to the object-side surface of the double-concave negativelens.

The lenses that form the zoom optical system of the example are allone-piece lenses except the image-side negative meniscus lens in thefirst lens group G1. Each one-piece lens has been fabricated by theprocess shown in FIG. 3.

One exemplary one-piece lens 10 used herein is shown in FIG. 19. FIG. 19is illustrative in section of the doublet in the first lens group G1,wherein the image-side double-convex positive lens is configured as theone-piece lens 10, with the negative meniscus lens cemented to theobject side thereof. The second lens blank 12 is 0.2 mm in thickness.Although not shown in FIG. 19, the second lens blank 12 could beprocessed simultaneously with the provision of a hole or an irregularpattern (see FIG. 3).

Numerical data on each example will be given later.

-   (3) Zoom optical system wherein the first group is a negative lens    group, the second group is a positive lens group and the third group    is a positive lens group

Examples 3-1 and 3-2 of the third zoom optical system (zoom lens) arenow explained with reference to the drawings. FIGS. 20 and 21 areillustrative in lens section along the optical axes of Examples 3-1 and3-2 at the wide-angle ends (a), in intermediate settings (b) and at thetelephoto ends (c), respectively, upon focusing on an infinite objectpoint. FIGS. 20 and 21 are aberration diagrams for spherical aberration,astigmatism and chromatic aberration of magnification of Examples 3-1and 3-2 at the wide-angle ends (a), in the intermediate settings (b) andat the telephoto ends (c), respectively, upon focusing on an infiniteobject point.

EXAMPLE 3-1

FIG. 20 is illustrative of the zoom optical system of Example 3-1, whichis made up of, in order from its object side, a first lens group G1, anaperture stop S, a second lens group G2 and a third lens group G3. Uponzooming from the wide-angle end to the telephoto end of the opticalsystem, the first lens group G1 moves in a concave locus toward theobject side and is located in the same position at the telephoto end asat the wide-angle end, and the second lens group moves in unison withthe aperture stop S toward the object side. The third lens group G3moves toward the image side of the optical system.

The first lens group G1 has generally negative power, and is composedof, in order from its object side, a negative meniscus lens convex onits object side and a positive meniscus lens concave on its image side.One spherical surface is applied to the image-side surface of thenegative meniscus lens.

The second lens group G2 has generally positive power, and is composedof, in order from its object side, a double-convex positive lens, adouble-concave negative lens and a double-convex positive lens. Oneaspheric surface is applied to the object-side surface of thedouble-convex positive lens nearest to the object side.

The third lens group G3 has positive power, and is composed of apositive meniscus lens concave on its image side. One aspheric surfaceis applied to the object-side surface of the positive meniscus lens.

The lenses that form the zoom optical system used herein are allone-piece lenses except the object-side negative meniscus lens in thefirst lens group G1. Each one-piece lens has been fabricated by theprocess shown in FIG. 1.

One exemplary one-piece lens 10 used herein is shown in FIG. 24. FIG. 24is illustrative in section of the image-side positive meniscus lens inthe first lens group G1. In this lens, the positive meniscus lens isconfigured as a one-piece lens. The second lens blank 12 is 0.45 mm inthickness. Although not depicted in FIG. 24, the second lens blank 12could be processed simultaneously with the provision of a hole or anirregular pattern.

EXAMPLE 3-2

FIG. 21 is illustrative of the zoom optical system of Example 3-2, whichis made up of, in order from its object side, a first lens group G1, anaperture stop S, a second lens group G2 and a third lens group G3. Uponzooming from the wide-angle end to the telephoto end of the opticalsystem, the first lens group G1 moves in a concave locus toward theobject side, and is located in much the same position at the telephotoend as at the wide-angle end, and the second lens group G2 moves inunison with the aperture stop S toward the object side. The third lensgroup G3 remains fixed.

The first lens group G1 has generally negative power, and is composed ofa doublet consisting of a double-concave negative lens and a positivemeniscus lens concave on its image side. One aspheric surface is appliedto the object-side surface of the double-concave negative lens.

The second lens group G2 has generally positive power, and is composedof, in order from its object side, a double-convex positive lens and adoublet consisting of a double-convex positive lens and a double-concavenegative lens. One aspheric surface is applied to the object-sidesurface of the double-convex positive lens nearest to the object side.

The third lens group G3 has positive power, and is composed of apositive meniscus lens concave on its object side. One aspheric surfaceis applied to the image-side surface of the positive meniscus lens.

The lenses that form the zoom optical system of the example are allone-piece lenses except the double-concave negative lens in the secondlens group G2. Each one-piece lens has been fabricated by the processshown in FIG. 3.

One exemplary one-piece lens 10 used herein is depicted in FIG. 25. FIG.25 is illustrative in section of the doublet in the second lens groupG2, wherein the object-side double-convex positive lens is configured asthe one-piece lens 10, with the double-concave negative lens cemented tothe image side thereof. The second lens blank 12 has a thickness of 0.3mm. Although not shown in FIG. 25, the second lens blank 12 could beprocessed simultaneously with the provision of a hole or an irregularpattern (see FIG. 3).

Numerical data on each example will be set out later.

-   (4) Zoom optical system wherein the first group is a negative lens    group, the second group is a positive lens group, the third group is    a positive lens group and the fourth group is a negative lens group

Examples 4-1 and 4-2 of the fourth zoom optical system (zoom lens) arenow explained with reference to the drawings. FIGS. 26 and 27 areillustrative in lens section along the optical axes of Examples 4-1 and4-2 at the wide-angle ends (a), in intermediate settings (b) and at thetelephoto ends (c), respectively, upon focusing on an infinite objectpoint. FIGS. 28 and 29 are aberration diagrams for spherical aberration,astigmatism, chromatic aberration of magnification and distortion ofExamples 4-1 and 4-2 at the wide-angle ends (a), in the intermediatesettings (b) and at the telephoto ends (c), respectively, upon focusingon an infinite object point.

EXAMPLE 4-1

FIG. 26 is illustrative of the zoom optical system of Example 4-1, whichis made up of, in order from its object side, a first lens group G1, anaperture stop S, a second lens group G2, a third lens group G3 and afourth lens group G4. Upon zooming from the wide-angle end to thetelephoto end of the optical system, the first lens group G1 moves in aconcave locus toward the object side and is located in much the sameposition at the telephoto end as at the wide-angle end; the second lensgroup G2 moves in unison with the aperture stop S toward the objectside; and the third and fourth lens groups G3 and G4 remain fixed.

The first lens group G1 has generally negative power, and is composedof, in order from its object side, a double-concave negative lens and apositive meniscus lens concave on its image side. One aspheric surfaceis applied to the image-side surface of the double-concave negativelens.

The second lens group G2 has generally positive power, and is composedof, in order from its object side, a double-convex positive lens and adoublet consisting of a double-convex positive lens and a double-concavenegative lens. Two aspheric surfaces are used: one at the object-sidesurface of the double-convex positive lens that is a single lens, andanother at the surface of the doublet nearest to its object side.

The third lens group G3 has positive power, and consists of adouble-convex positive lens. The third lens group G3 moves in theoptical axis direction upon focusing alone.

The fourth lens group G4 has negative power, and consists of a negativemeniscus lens convex on its image side. One aspheric surface is appliedto the image-side surface of the negative meniscus lens.

The lenses that form the zoom optical system of the example are allone-piece lenses. Each one-piece lens has been fabricated by the processshown in FIG. 1.

One exemplary one-piece lens 10 used herein is shown in FIG. 30. FIG. 30is illustrative in section of the second lens as counted from the objectside of the first lens group G1, wherein the positive meniscus lens isconfigured as the one-piece lens. The second lens blank 12 is 0.4 mm inthickness. Although not shown in FIG. 30, the second lens blank 12 couldbe processed simultaneously with the provision of a hole or an irregularpattern.

EXAMPLE 4-2

FIG. 27 is illustrative of the zoom optical system of the example, whichis made up of, in order from its object side, a first lens group G1, asecond lens group G2, a third lens group G3 and a fourth lens group G4.An aperture stop S is interposed between the first lens and the secondlens in the second lens group G1 in an integration fashion with them.Upon zooming from the wide-angle end to the telephoto end of the opticalsystem, the first lens group G1 moves in a concave locus toward theobject side and is located in much the same position at the telephotoend as at the wide-angle end; the second lens group G2 moves in unisonwith the apertures stop S toward the object side; and the third andfourth lens groups G3 and G4 remain stationary.

The first lens group G1 has generally negative power, and is composed ofa doublet consisting of a double-concave negative lens and a positivemeniscus lens concave on its image side.

The second lens group G2 has generally positive power, and is composedof, in order from its object side, a positive meniscus lens concave onits image side, an aperture stop S and a doublet consisting of adouble-convex positive lens and a double-concave negative lens. Threeaspheric surfaces are used: one at the object-side surface of thepositive meniscus lens and two at the surfaces of the doublet nearest toits object and image sides.

The third lens group G3 has positive power, and consists of a positivemeniscus lens convex on its image side. The third lens group G3 moves inthe optical axis direction upon focusing alone.

The fourth lens group G4 has negative power, and consists of a negativemeniscus lens convex on its image side. One aspheric surface is appliedto the image-side surface of the negative meniscus lens.

The lenses that form the zoom optical system of the example are allone-piece lenses except the double-concave negative lens in the firstlens group G1. Each one-piece lens has been fabricated by the processshown in FIG. 3.

One exemplary one-piece lens 10 used herein is shown in FIG. 31. FIG. 31is illustrative in section of the doublet in the first lens group G1. Inthis doublet, the image-side positive meniscus lens is configured as theone-piece lens 10, with the double-concave negative lens cemented to theobject side thereof. The second lens blank 12 is 0.3 mm in thickness.Although not depicted in FIG. 31, the second lens blank 12 could beprocessed simultaneously with the provision of a hole or an irregularpattern (see FIG. 3).

Numerical data on each example will be set out later.

-   (5) Zoom optical system wherein the first group is a negative lens    group, the second group is a positive lens group, the third group is    a negative lens group and the fourth group is a positive lens group

Examples 5-1 and 5-2 of the fifth zoom optical system (zoom lens) arenow explained with reference to the drawings. FIGS. 32 and 33 areillustrative in lens section along the optical axes of Examples 5-1 and5-2 at the wide-angle ends (a), in intermediate settings (b) and at thetelephoto ends (c), respectively, upon focusing on an infinite objectpoint. FIGS. 34 and 35 are aberration diagrams for spherical aberration,astigmatism, chromatic aberration of magnification and distortion ofExamples 5-1 and 5-2 at the wide-angle ends (a), in the intermediatesettings (b) and at the telephoto ends (c), respectively, upon focusingon an infinite object point.

EXAMPLE 5-1

FIG. 32 is illustrative of the zoom optical system of this example,which is made up of, in order from its object side, a first lens groupG1, a second lens group G2, an aperture stop S, a third lens group G3and a fourth lens group G4. Upon zooming from the wide-angle end to thetelephoto end of the optical system, the first lens group G1 remainsfixed; the second lens group G2 moves in unison with the aperture stop Stoward the object side; the third lens group G3 moves toward the objectside while the space between it and the fourth lens group G4 firstbecomes narrow and then wide; and the fourth lens group G4 remainsfixed.

The first lens group G1 has generally negative power, and is composed ofa doublet consisting of a double-concave negative lens and a positivemeniscus lens concave on its image side. Three aspheric surfaces areused: one at the object-side surface of the double-convex positive lens,and two at the surfaces of the doublet nearest to its object and imagesides.

The second lens group G2 has generally positive power, and is composedof, in order from its object side, a double-convex positive lens and adoublet consisting of a double-convex positive lens and a double-concavenegative lens. Three aspheric surfaces are used: one at the object-sidesurface of the double-convex positive lens, and two at the surfaces ofthe doublet nearest to its object and image sides.

The third lens group G3 has negative power, and consists of a negativemeniscus lens convex on its object side. One aspheric surface is appliedto the image-side surface of the negative meniscus lens.

The fourth lens group G4 has positive power, and consists of a positivemeniscus lens concave on its object side. One aspheric surface isapplied to the image-side surface of the positive meniscus lens.

The lenses that form the zoom optical system of this example are allone-piece lenses except the negative meniscus lens in the third lensgroup G3. Each one-piece lens has been fabricated by the process shownin FIG. 1.

One exemplary one-piece lens 10 used herein is depicted in FIG. 36. FIG.36 is illustrative in section of the object-side double-convex positivelens in the second lens group G2. In this lens, the double-convexpositive lens is configured as the one-piece lens. The second lens blank12 is 0.4 mm in thickness. Although not shown in FIG. 36, the secondlens blank 12 could be processed simultaneously with the provision of ahole or an irregular pattern.

EXAMPLE 5-2

FIG. 33 is illustrative of the zoom optical system of this example,which is made up of, in order from its object side, a first lens groupG1, a second lens group G2, an aperture stop S, a third lens group G3and a fourth lens group G4. Upon zooming from the wide-angle end to thetelephoto end of the optical system, the first lens group G1 remainsfixed; the second lens group G2 moves in unison with the aperture stop Stoward the object side; the third lens group G3 moves toward the objectside while the space between it and the fourth lens group G4 firstbecomes slightly narrow and then wide; and the fourth lens group G4remains fixed.

The first lens group G1 has generally negative power, and is composed ofa doublet consisting of a double-concave negative lens and a positivemeniscus lens concave on its image side. Two aspheric surfaces are usedat the surfaces of the doublet nearest to its object and image sides.

The second lens group G2 has generally positive power, and is composedof, in order from its object side, a double-convex positive lens and adoublet consisting of a double-convex positive lens and a double-concavenegative lens. Three aspheric surfaces are used: one at the object-sidesurface of the double-convex positive lens that is a single lens, andtwo at the surfaces of the doublet nearest to its object and imagesides.

The third lens group G3 has negative power, and consists of adouble-concave negative lens. One aspheric surface is applied to theimage-side surface of the double-convex positive lens.

The fourth lens group G4 has positive power, and consists of adouble-convex positive lens. One aspheric surface is applied to theimage-side surface of the double-convex positive lens.

The lenses that form the zoom optical system of this example are allone-piece lenses except the double-concave negative lens in the secondlens group G2. Each one-piece lens has been fabricated by the processshown in FIG. 3.

One exemplary one-piece lens 10 used herein is depicted in FIG. 37. FIG.37 is illustrative in section of the doublet in the second lens groupG2. In this doublet, the object-side double-convex positive lens isconfigured as the one-piece lens 10, with the double-concave negativelens cemented to the image side thereof. The second lens blank 12 has athickness of 0.5 mm. Although not depicted in FIG. 37, the second lensblank 12 could be processed simultaneously with the provision of a holeor an irregular pattern (see FIG. 3).

Numerical data on each example will be given later.

-   (6) Zoom optical system wherein the first group is a negative lens    group, the second group is a positive lens group, the third group is    a positive lens group and the fourth group is a positive lens group

Examples 6-1, 6-2 and 6-3 of the sixth zoom optical system (zoom lens)are now explained with reference to the drawings. FIGS. 38, 39 and 40are illustrative in lens section along the optical axes of Examples 6-1,6-2 and 6-3 at the wide-angle ends (a), in intermediate settings (b) andat the telephoto ends (c), respectively, upon focusing on an infiniteobject point. FIGS. 41, 42 and 43 are aberration diagrams for sphericalaberration, astigmatism, chromatic aberration of magnification anddistortion of Examples 6-1, 6-2 and 6-3 at the wide-angle ends (a), inthe intermediate settings (b) and at the telephoto ends (c),respectively, upon focusing on an infinite object point.

EXAMPLE 6-1

FIG. 38 is illustrative of the zoom optical system of this example,which is made up of, in order from its object side, a first lens groupG1, an aperture stop S, a second lens group G2, a third lens group G3and a fourth lens group G4. Upon zooming from the wide-angle end to thetelephoto end of the optical system, the first lens group G1 moves in aconcave locust toward the object side and is located in much the sameposition at the telephoto end as at the wide-angle end. The second lensgroup G2 moves in unison with the aperture stop S toward the objectside. The third lens group moves slightly toward the object side. Thefourth lens group G4 moves in a convex locus slightly toward the objectside, and is located nearer to the image side of the optical system atthe telephoto end than at the wide-angle end.

The first lens group G1 has generally negative power, and is composedof, in order from its object side, a double-concave negative lens and apositive meniscus lens concave on its image side. One aspheric surfaceis applied to the image-side surface of the double-concave negativelens.

The second lens group G2 has generally positive power, and is composedof, in order from its object side, a double-convex positive lens and adoublet consisting of a double-convex positive lens and a double-concavenegative lens. Two aspheric surfaces are used: one at the object-sidesurface of the double-convex positive lens and one at the surface of thedoublet nearest to its object side.

The third lens group G3 has positive power, and consists of a positivemeniscus lens concave on its image side. One aspheric surface is appliedto the image-side surface of the positive meniscus lens.

The fourth lens group G4 has positive power, and consists of aplano-convex positive lens convex on its image side. One asphericsurface is applied to the image-side surface of the plano-convexpositive lens.

The lenses that form the zoom optical system of this example are allone-piece lenses except the double-concave negative lens in the secondlens group G2. Each one-piece lens has been fabricated by the processshown in FIG. 1.

One exemplary one-piece lens 10 used herein is shown in FIG. 44. FIG. 44is illustrative in section of the doublet in the second lens group G2.In this doublet, the object-side double-convex positive lens isconfigured as the one-piece lens 10, with the double-concave negativelens cemented to the image side thereof. The second lens blank 12 is0.35 mm in thickness. Although not depicted in FIG. 44, the second lensblank 12 could be processed simultaneously with the provision of a holeor an irregular pattern.

EXAMPLE 6-2

FIG. 39 is illustrative of the zoom optical system of this example,which is made up of, in order from its object side, a first lens groupG1, an aperture stop S, a second lens group G2, a third lens group G3and a fourth lens group G4. Upon zooming from the wide-angle end to thetelephoto end of the optical system, the first lens group G1 moves in aconcave locust toward the object side and is located in much the sameposition at the telephoto end as at the wide-angle end. The second lensgroup G2 moves in unison with the aperture stop S toward the objectside. The third lens group G3 moves toward the object side while thespace between it and the second lens group G2 becomes wide. The fourthlens group G4 moves in a convex locus toward the object side and ispositioned nearer to the image side of the optical system at thetelephoto end than at the wide-angle end.

The first lens group G1 has generally negative power, and is composedof, in order from its object side, a plane-concave negative lens concaveon its image side and a positive meniscus lens concave on its imageside. One aspheric surface is applied to the image-side surface of theplano-concave negative lens.

The second lens group G2 has generally positive power, and is composedof, in order from its object side, a double-convex positive lens and adoublet consisting of a double-convex positive lens and a double-concavenegative lens. Two aspheric surfaces are used: one at the object-sidesurface of the object-side double-convex positive lens and one at thesurface of the doublet nearest to its object side.

The third lens group G3 has positive power, and consists of a positivemeniscus lens concave on its image side. One aspheric surface is appliedto the image-side surface of the positive meniscus lens.

The fourth lens group G4 has positive power, and consists of a positivemeniscus lens concave on its object side. One aspheric surface isapplied to the image-side surface of the positive meniscus lens.

The lenses that form the zoom optical system of this example are allone-piece lenses that have been fabricated by the process shown in FIG.3.

One exemplary one-piece lens 10 used herein is shown in FIG. 45. FIG. 45is illustrative in section of the positive meniscus lens in the firstlens group G1. In this lens, the positive meniscus lens is configured asthe one-piece lens 10. The second lens blank 12 is 0.5 mm in thickness.Although not depicted in FIG. 45, the second lens blank 12 could beprocessed simultaneously with the provision of a hole or an irregularpattern (see FIG. 3).

EXAMPLE 6-3

FIG. 40 is illustrative of the zoom optical system of this example,which is made up of, in order from its object side, a first lens groupG1, an aperture stop S, a second lens group G2, a third lens group G3and a fourth lens group G4. Upon zooming from the wide-angle end to thetelephoto end of the optical system, the first lens group G1 moves in aconcave locus toward the object side and is located in much the sameposition at the telephoto end as at the wide-angle end. The second lensgroup G2 moves in unison with the aperture stop S toward the objectside. The third lens group G3 moves in a concave locus toward the objectside and is positioned nearer to the object side at the telephoto endthan at the wide-angle end. The fourth lens group G4 remains fixed.

The first lens group G1 has generally negative power, and is composedof, in order from its object side, a double-concave negative lens and apositive meniscus lens concave on its image side. One aspheric surfaceis applied to the image-side surface of the double-concave negativelens.

The second lens group G2 has generally positive power, and is composedof, in order from its object side, a double-convex positive lens and adoublet consisting of a double-convex positive lens and a double-concavenegative lens. Two aspheric surfaces are used: one at the object-sidesurface of the object-side double-convex positive lens and one at thesurface of the doublet nearest to its object side.

The third lens group G3 has positive power, and consists of a positivemeniscus lens concave on its image side. One aspheric surface is appliedto the image-side surface of the positive meniscus lens.

The fourth lens group G4 has positive power, and consist of a positivemeniscus lens concave on its image side. One aspheric surface is appliedto the image-side surface of the positive meniscus lens.

The lenses that form the zoom optical system of this example are allone-piece lenses except the double-concave negative lens in the secondlens group G2. Each one-piece lens has been fabricated by the processshown in FIG. 5.

One exemplary one-piece lens 10 used herein is shown in FIG. 46. FIG. 46is illustrative in section of the doublet in the second lens group G2.In this doublet, the object-side double-convex positive lens isconfigured as the one-piece lens 10, with the double-concave negativelens cemented to the image side thereof. The second lens blank 12 is 0.3mm in thickness. Although not depicted in FIG. 46, the second lens blank12 could be processed simultaneously with the formation of a hole or anirregular pattern (see FIG. 3).

Numerical data on each example will be given later.

-   (7) Zoom optical system wherein the first group is a positive lens,    the second group is a negative lens group, the third group is a    positive lens group and the fourth group is a positive lens group

Examples 7-1, 7-2 and 7-3 of the sixth zoom optical system (zoom lens)are now explained with reference to the drawings. FIGS. 47, 48 and 49are illustrative in lens section along the optical axes of Examples 7-1,7-2 and 7-3 at the wide-angle ends (a), in intermediate settings (b) andat the telephoto ends (c), respectively, upon focusing on an infiniteobject point. FIGS. 50, 51 and 52 are aberration diagrams for sphericalaberration, astigmatism, chromatic aberration of magnification anddistortion of Examples 7-1, 7-2 and 7-3 at the wide-angle ends (a), inthe intermediate settings (b) and at the telephoto ends (c),respectively, upon focusing on an infinite object point.

EXAMPLE 7-1

FIG. 47 is illustrative of the zoom optical system of this example,which is made up of, in order from its object side, a first lens groupG1, a second lens group G2, an aperture stop S, a third lens group G3and a fourth lens group G4. Upon zooming from the wide-angle end to thetelephoto end of the optical system, the first lens group G1 remainsfixed; the second lens group G2 moves toward the image side of theoptical system; the aperture stop S moves toward the object side; andboth the third and fourth lens groups G3 and G4 moves toward the objectside. In the meantime, the third and fourth lens groups G3 and G4 movewhile their space becomes wide.

The first lens group G1 has generally positive power, and consists of adouble-convex positive lens. One aspheric surface is applied to theobject-side surface of the double-convex positive lens.

The second lens group G2 has generally negative power, and is composedof a doublet consisting of a double-concave negative lens and a positivemeniscus lens concave on its image side. One aspheric surface is appliedto the surface of the doublet nearest to its object side.

The third lens group G3 has positive power, and is composed of, in orderfrom its object side, a double-convex positive lens and a double-concavenegative lens. Two aspheric surfaces are used: one at the object-sidesurface of the double-convex positive lens and another at the image-sidesurface of the double-concave negative lens.

The fourth lens group G4 has positive power, and consists of adouble-convex positive lens. One aspheric surface is applied to theobject-side surface of the double-convex positive lens.

The lenses that form the zoom optical system of this example are allone-piece lenses that have been fabricated by the process illustrated inFIG. 1.

One exemplary one-piece lens 10 used herein is shown in FIG. 53. FIG. 53is illustrative in section of the double-convex positive lens in thefourth lens group G4, which is configured as a one-piece lens. Thesecond lens blank 12 is 0.4 mm in thickness. Although not shown in FIG.53, the second lens blank 12 could be processed simultaneously with theformation of a hole or an irregular pattern.

EXAMPLE 7-2

FIG. 48 is illustrative of the zoom optical system of this example,which is made up of, in order from its object side, a first lens groupG1, a second lens group G2, an aperture stop S, a third lens group G3and a fourth lens group G4. Upon zooming from the wide-angle end to thetelephoto end of the optical system, the first lens group G1 remainsfixed; the second lens group G2 moves toward the image side of theoptical system; the aperture stop S moves toward the object side; andboth the third and fourth lens groups G3 and G4 move toward the objectside while their space becomes wide.

The first lens group G1 generally positive power, and consists of adouble-convex positive lens. One aspheric surface is applied to theobject-side surface of the double-convex positive lens.

The second lens group G2 has generally negative power, and consists of adouble-concave negative lens and a positive meniscus lens concave on itsimage side. One aspheric surface is applied to the object-side surfaceof the double-concave negative lens.

The third lens group G3 has positive power, and is composed of, in orderfrom its object side, a double-convex positive lens and a double-concavenegative lens. Two aspheric surfaces are used: one at the object-sidesurface of the double-convex positive lens and another at the image-sidesurface of the double-concave negative lens.

The fourth lens group G4 has positive power, and consists of a positivemeniscus lens concave on its image side. One aspheric surface is appliedto the object-side surface of the positive meniscus lens.

The lenses that form the zoom optical system of this example are allone-piece lenses that have been fabricated by the process shown in FIG.3.

Exemplary one-piece lenses used herein are shown in FIGS. 54 and 55.FIG. 54 is illustrative in section of the positive meniscus lens in thesecond lens group G2, which is configured as the one-piece lens 10. Thesecond lens blank 12 has a thickness of 0.4 mm. FIG. 55 is illustrativein section of the double-concave negative lens in the third lens groupG3, which is configured as a one-piece lens. The second lens blank 12 is1.2 mm in thickness. Although not shown in FIGS. 54 and 55, the secondlens blank 12 could be processed simultaneously with the formation of ahole or an irregular pattern (see FIG. 3).

EXAMPLE 7-3

FIG. 49 is illustrative of the zoom optical system of this example,which is made up of, in order from its object side, a first lens groupG1, a second lens group G2, an aperture stop S, a third lens group G3and a fourth lens group G4. Upon zooming from the wide-angle end to thetelephoto end of the optical system, the first lens group G1 remainsfixed; the second lens group G2 moves toward the image side of theoptical system; the aperture stop S remains fixed; the third lens groupG3 moves toward the object side; and the fourth lens group G4 moves in aconvex locus toward the object side. It is here noted that the fourthlens group G4 is positioned nearer to the image side at the telephotoend than at the wide-angle end.

The first lens group G1 has generally positive power, and consists of adouble-convex positive lens. One aspheric surface is applied to theobject-side surface of the double-convex positive lens.

The lens group G2 has generally negative power, and is composed of, inorder from its object side, a double-concave negative lens and apositive meniscus lens concave on its image side. One aspheric surfaceis applied to the object-side surface of the double-concave negativelens.

The third lens group G3 has positive power, and is composed of, in orderfrom its object side, a double-convex positive lens and a double-concavenegative lens. Two aspheric surfaces are used: one at the object-sidesurface of the double-convex positive lens and another at the image-sidesurface of the double-concave negative lens.

The fourth lens group G4 has positive power, and consists of a positivemeniscus lens concave on its image side. One aspheric surface is appliedto the object-side surface of the positive meniscus lens.

The lenses that form the zoom optical system of this example are allone-piece lenses that have been fabricated by the process illustrated inFIG. 5.

One exemplary one-piece lens 10 used herein is illustrated in FIG. 56.FIG. 56 is illustrative of the positive meniscus lens in the fourth lensgroup G4, which is configured as a one-piece lens. The second lens blank12 is 0.3 mm in thickness. Although not shown in FIG. 56, the secondlens blank 12 could be processed simultaneously with the formation of ahole or an irregular pattern (see FIG. 3).

The numerical data on each example are now set out. However, it is notedthat the symbols used hereinafter but not hereinbefore have thefollowing meanings.

f: focal length of the zoom optical system,

f_(NO): F-number,

ω: half angle of view,

WE: wide-angle end,

ST: intermediate setting,

TE: telephoto end,

r₁, r₂, . . . : radius of curvature of each lens surface,

d₁, d₂, . . . : space between adjacent lens surfaces,

n_(d1), n_(d2), . . . : d-line refractive index of each lens, and

ν_(d1), ν_(d2), . . . : Abbe constant of each lens.

Note that the aspheric shape is given by the following formula, providedthat x is an optical axis where the direction of travel of light istaken as positive, and y is a direction orthogonal to the optical axis.x=(y ² /r)/[1+{1−(K+1)(y/r)²}^(1/2)]+A ₄ y ⁴ +A ₆ y ⁶ +A ₈ y ⁸ A ₁₀ y ¹⁰Here r is a paraxial radius of curvature, K is a conical coefficient,and A₄, A₆, A₈ and A₁₀ are the 4^(th)-, 6^(th)-, 8^(th)- and10^(th)-order aspheric coefficients, respectively.

EXAMPLE 1-1

r₁ = −41.781 d₁ = 0.60 n_(d1) = 1.80610 ν_(d1) = 40.92 (Aspheric) r₂ =3.177 (Aspheric) d₂ = 0.66 r₃ = 6.332 d₃ = 0.62 n_(d2) = 1.84666 ν_(d2)= 23.78 r₄ = 24.596 d₄ = (Variable) r₅ = ∞ (Stop) d₅ = 0.10 r₆ = 2.662(Aspheric) d₆ = 0.95 n_(d3) = 1.51633 ν_(d3) = 64.14 r₇ = −6.827 d₇ =0.10 r₈ = 9.099 d₈ = 0.86 n_(d4) = 1.80610 ν_(d4) = 40.92 r₉ = −2.887 d₉= 0.61 n_(d5) = 1.68893 ν_(d5) = 31.07 r₁₀ = 3.039 (Aspheric) d₁₀ =(Variable) r₁₁ = ∞ d₁₁ = 0.50 n_(d6) = 1.51633 ν_(d6) = 64.14 r₁₂ = ∞Aspherical Coefficients 1st surface K = 298.089 A₄ = −1.32975 × 10⁻² A₆= 2.40059 × 10⁻³ A₈ = −1.12956 × 10⁻⁴ A₁₀ = 0 2nd surface K = −6.673 A₄= 7.26462 × 10⁻³ A₆ = −2.67280 × 10⁻³ A₈ = 1.15842 × 10⁻³ A₁₀ = −1.24655× 10⁻⁴ 6th surface K = −1.680 A₄ = 3.59073 × 10⁻³ A₆ = −9.37097 × 10⁻⁴A₈ = 1.54936 × 10⁻⁴ A₁₀ = −3.54681 × 10⁻⁵ 10th surface K = 1.840 A₄ =6.69764 × 10⁻³ A₆ = 0 A₈ = 0 A₁₀ = 0 Zooming Data (∞) WE ST TE f (mm)4.4 6.23 8.78 F_(NO) 2.8 3.3 4.1 ω (°) 33.2 22.5 15.9 d₄ 3.16 1.38 0.14d₁₀ 4.24 5.47 7.26

EXAMPLE 1-2

r₁ = −20.127 (Aspheric) d₁ = 0.60 n_(d1) = 1.67790 ν_(d1) = 55.34 r₂ =2.853 d₂ = 1.23 r₃ = 4.097 d₃ = 0.72 n_(d2) = 1.84666 ν_(d2) = 23.78 r₄= 5.809 d₄ = (Variable) r₅ = ∞ (Stop) d₅ = 0.10 r₆ = 2.549 (Aspheric) d₆= 0.84 n_(d3) = 1.69350 ν_(d3) = 53.21 r₇ = −3.172 d₇ = 0.60 n_(d4) =1.80518 ν_(d4) = 25.42 r₈ = −9.327 d₈ = 1.04 r₉ = −3.278 d₉ = 0.60n_(d5) = 1.81474 ν_(d5) = 37.03 r₁₀ = −7.604 (Aspheric) d₁₀ = (Variable)r₁₁ = ∞ d₁₁ = 0.50 n_(d6) = 1.51633 ν_(d6) = 64.14 r₁₂ = ∞ AsphericalCoefficients 1st surface K = −228.497 A₄ = −1.41365 × 10⁻³ A₆ = 1.48862× 10⁻⁴ A₈ = −4.35387 × 10⁻⁶ A₁₀ = 0 6th surface K = −0.176 A₄ = −4.34973× 10⁻⁴ A₆ = 1.10461 × 10⁻⁴ A₈ = 2.52554 × 10⁻⁴ A₁₀ = −1.39801 × 10⁻⁴10th surface K = −7.497 A₄ = 1.45179 × 10⁻² A₆ = 7.85336 × 10⁻⁴ A₈ =2.70499 × 10⁻³ A₁₀ = −5.60770 Zooming Data (∞) WE ST TE f (mm) 3.0 5.29.0 F_(NO) 3.5 4.5 6.3 ω (°) 50.4 26.7 15.6 d₄ 5.05 1.96 0.19 d₁₀ 3.064.82 7.93

EXAMPLE 2-1

r₁ = ∞ (Stop) d₁ = 0.55 r₂ = −2.158 (Aspheric) d₂ = 0.69 n_(d1) =1.49700 ν_(d1) = 81.54 r₃ = −2.071 (Aspheric) d₃ = 0.10 r₄ = 10.989 d₄ =0.60 n_(d2) = 1.84666 ν_(d2) = 23.78 r₅ = 4.313 d₅ = 0.12 r₆ = 4.932 d₆= 1.16 n_(d3) = 1.51633 ν_(d3) = 64.14 r₇ = −2.401 (Aspheric) d₇ =(Variable) r₈ = −6.483 d₈ = 0.62 n_(d4) = 1.84666 ν_(d4) = 23.78 r₉ =−3.958 d₉ = 0.79 r₁₀ = −2.597 (Aspheric) d₁₀ = 0.60 n_(d5) = 1.80610ν_(d5) = 40.92 r₁₁ = 61.065 d₁₁ = (Variable) r₁₂ = ∞ d₁₂ = 0.50 n_(d6) =1.51633 ν_(d6) = 64.14 r₁₃ = ∞ Aspherical Coefficients 2nd surface K =0.000 A₄ = −2.84390 × 10⁻² A₆ = 9.11709 × 10⁻³ A₈ = 7.00659 × 10⁻³ A₁₀ =0 3rd surface K = −0.894 A₄ = −6.81547 × 10⁻³ A₆ = 5.63263 × 10⁻³ A₈ =5.81608 × 10⁻³ A₁₀ = 0 7th surface K = −0.359 A₄ = −4.65568 × 10⁻³ A₆ =−1.56716 × 10⁻³ A₈ = 1.86252 × 10⁻⁴ A₁₀ = −7.14500 × 10⁻⁵ 10th surface K= −4.566 A₄ = −2.78392 × 10⁻² A₆ = 4.86515 × 10⁻³ A₈ = −5.40423 × 10⁻⁴A₁₀ = 0 Zooming Data (∞) WE ST TE f (mm) 5.5 7.8 10.9 F_(NO) 2.8 4.0 5.5ω (°) 25.3 18.0 13.0 d₇ 1.71 0.76 0.10 d₁₁ 0.49 3.03 6.62

EXAMPLE 2-2

r₁ = ∞ (Stop) d₁ = 0.61 r₂ = −2.480 (Aspheric) d₂ = 0.60 n_(d1) =1.49700 ν_(d1) = 81.54 r₃ = −2.820 (Aspheric) d₃ = 0.63 r₄ = 8.606 d₄ =0.60 n_(d2) = 1.68893 ν_(d2) = 31.07 r₅ = 2.625 d₅ = 1.24 n_(d3) =1.58913 ν_(d3) = 61.14 r₆ = −2.953 (Aspheric) d₆ = (Variable) r₇ =−7.436 d₇ = 0.63 n_(d4) = 1.84666 ν_(d4) = 23.78 r₈ = −4.115 d₈ = 0.73r₉ = −2.736 (Aspheric) d₉ = 0.60 n_(d5) = 1.80610 ν_(d5) = 40.92 r₁₀ =26.678 d₁₀ = (Variable) r₁₁ = ∞ d₁₁ = 0.50 n_(d6) = 1.51633 ν_(d6) =64.14 r₁₂ = ∞ Aspherical Coefficients 2nd surface K = 0.000 A₄ =−5.18890 × 10⁻³ A₆ = 6.43068 × 10⁻³ A₈ = 2.08572 × 10⁻³ A₁₀ = 0 3rdsurface K = −1.389 A₄ = −3.33499 × 10⁻⁴ A₆ = 5.27759 × 10⁻³ A₈ = 2.05797× 10⁻³ A₁₀ = 0 6th surface K = −0.816 A₄ = −2.04253 × 10⁻³ A₆ = −1.18792× 10⁻³ A₈ = 3.09456 × 10⁻⁴ A₁₀ = −7.24211 × 10⁻⁵ 9th surface K = −3.385A₄ = −1.65664 × 10⁻² A₆ = 1.45807 × 10⁻³ A₈ = −8.20014 × 10⁻⁵ A₁₀ = 0Zooming Data (∞) WE ST TE f (mm) 5.5 7.78 10.96 F_(NO) 2.8 4.0 5.6 ω (°)25.2 18.0 12.9 d₆ 1.82 0.81 0.10 d₁₀ 0.39 2.92 6.55

EXAMPLE 3-1

r₁ = 12.646 d₁ = 0.60 n_(d1) = 1.69350 ν_(d1) = 53.21 r₂ = 3.067(Aspheric) d₂ = 1.08 r₃ = 4.805 d₃ = 0.75 n_(d2) = 1.84666 ν_(d2) =23.78 r₄ = 7.074 d₄ = (Variable) r₅ = ∞ (Stop) d₅ = 0.10 r₆ = 3.743(Aspheric) d₆ = 0.80 n_(d3) = 1.67790 ν_(d3) = 55.34 r₇ = −15.671 d₇ =0.89 r₈ = −5.791 d₈ = 0.60 n_(d4) = 1.76182 ν_(d4) = 26.52 r₉ = 4.399 d₉= 0.39 r₁₀ = 14.092 d₁₀ = 0.96 n_(d5) = 1.78590 ν_(d5) = 44.20 r₁₁ =−4.706 d₁₁ = (Variable) r₁₂ = 5.551 (Aspheric) d₁₂ = 0.80 n_(d6) =1.78800 ν_(d6) = 47.37 r₁₃ = 6.983 d₁₃ = (Variable) r₁₄ = ∞ d₁₄ = 0.50n_(d7) = 1.51633 ν_(d7) = 64.14 r₁₅ = ∞ Aspherical Coefficients 2ndsurface K = −1.200 A₄ = 3.55109 × 10⁻³ A₆ = 2.56305 × 10⁻⁴ A₈ = −2.33716× 10⁻⁵ A₁₀ = 2.07830 × 10⁻⁶ 6th surface K = −0.728 A₄ = 7.03429 × 10⁻⁴A₆ = −1.42131 × 10⁻⁵ A₈ = 5.98131 × 10⁻⁵ A₁₀ = −1.12393 × 10⁻⁵ 12thsurface K = −3.851 A₄ = 1.74180 × 10⁻³ A₆ = 8.82987 × 10⁻⁶ A₈ = 0 A₁₀ =0 Zooming Data (∞) WE ST TE f (mm) 4.4 6.2 8.8 F_(NO) 2.8 3.2 4.0 ω (°)30.8 22.3 15.7 d₄ 4.77 1.78 0.22 d₁₁ 0.10 2.61 8.22 d₁₃ 4.13 3.49 0.56

EXAMPLE 3-2

r₁ = −6.951 (Aspheric) d₁ = 0.60 n_(d1) = 1.67790 ν_(d1) = 55.34 r₂ =6.574 d₂ = 0.64 n_(d2) = 1.84666 ν_(d2) = 23.78 r₃ = 15.485 d₃ =(Variable) r₄ = ∞ (Stop) d₄ = 0.10 r₅ = 4.706 (Aspheric) d₅ = 0.69n_(d3) = 1.69350 ν_(d3) = 53.21 r₆ = −6.848 d₆ = 0.17 r₇ = 6.792 d₇ =0.92 n_(d4) = 1.80610 ν_(d4) = 40.92 r₈ = −2.029 d₈ = 0.60 n_(d5) =1.68893 ν_(d5) = 31.07 r₉ = 2.447 d₉ = (Variable) r₁₀ = −5.488 d₁₀ =0.77 n_(d6) = 1.68893 ν_(d6) = 31.07 r₁₁ = −3.434 (Aspheric) d₁₁ = 1.78r₁₂ = ∞ d₁₂ = 0.50 n_(d7) = 1.51633 ν_(d7) = 64.14 r₁₃ = ∞ AsphericalCoefficients 1st surface K = −4.615 A₄ = −1.30227 × 10⁻³ A₆ = 0 A₈ = 0A₁₀ = 0 5th surface K = −3.406 A₄ = −3.94764 × 10⁻³ A₆ = −7.90797 × 10⁻⁴A₈ = 2.03424 × 10⁻⁴ A₁₀ = −1.31727 × 10⁻⁴ 11th surface K = −0.035 A₄ =3.45595 × 10⁻³ A₆ = 0 A₈ = 0 A₁₀ 0 Zooming Data (∞) WE ST TE f (mm) 4.46.2 8.8 F_(NO) 2.8 3.3 4.1 ω (°) 32.9 21.8 15.4 d₃ 3.26 1.43 0.14 d₉1.88 3.18 4.99

EXAMPLE 4-1

r₁ = −8.544 d₁ = 0.60 n_(d1) = 1.69350 ν_(d1) = 53.21 r₂ = 5.795(Aspheric) d₂ = 0.44 r₃ = 7.279 d₃ = 0.67 n_(d2) = 1.84666 ν_(d2) =23.78 r₄ = 19.919 d₄ = (Variable) r₅ = ∞ (Stop) d₅ = 0.10 r₆ = 3.655(Aspheric) d₆ = 1.38 n_(d3) = 1.69350 ν_(d3) = 53.21 r₇ = −14.166 d₇ =0.10 r₈ = 9.263 (Aspheric) d₈ = 0.99 n_(d4) = 1.78800 ν_(d4) = 47.37 r₉= −2.793 d₉ = 0.60 n_(d5) = 1.68893 ν_(d5) = 31.07 r₁₀ = 3.038 d₁₀ =(Variable) r₁₁ = 44.064 d₁₁ = 1.60 n_(d6) = 1.78800 ν_(d6) = 47.37 r₁₂ =−4.323 d₁₂ = 0.16 r₁₃ = −3.912 d₁₃ = 1.60 n_(d7) = 1.51633 ν_(d7) =64.14 r₁₄ = −18.192 (Aspheric) d₁₄ = 0.10 r₁₅ = ∞ d₁₅ = 0.50 n_(d8) =1.51633 ν_(d8) = 64.14 r₁₆ = ∞ Aspherical Coefficients 2nd surface K =−0.856 A₄ = −5.31098 × 10⁻⁴ A₆ = 2.90922 × 10⁻⁴ A₈ = −6.35097 × 10⁻⁵ A₁₀= 5.38366 × 10⁻⁶ 6th surface K = 0.057 A₄ = −2.33967 × 10⁻⁴ A₆ = 6.09317× 10⁻⁶ A₈ = 8.12573 × 10⁻⁵ A₁₀ = −1.66984 × 10⁻⁵ 8th surface K = −33.940A₄ = −1.48982 × 10⁻³ A₆ = −1.35589 × 10⁻³ A₈ = 0 A₁₀ = 0 14th surface K= 0.000 A₄ = 7.17227 × 10⁻³ A₆ = −6.23670 × 10⁻⁴ A₈ = 0 A₁₀ = 0 ZoomingData (∞) WE ST TE f (mm) 4.4 6.2 8.8 F_(NO) 2.8 3.3 4.1 ω (°) 33.1 22.115.6 d₄ 3.63 1.58 0.14 d₁₀ 2.14 3.59 5.65

EXAMPLE 4-2

r₁ = −6.328 d₁ = 0.60 n_(d1) = 1.69350 ν_(d1) = 53.21 r₂ = 3.092 d₂ =1.03 n_(d2) = 1.81474 ν_(d2) = 37.03 r₃ = 11.872 d₃ = (Variable) r₄ =3.024 (Aspheric) d₄ = 1.08 n_(d3) = 1.69350 ν_(d3) = 53.21 r₅ = 36.382d₅ = 0.12 r₆ = ∞ (Stop) d₆ = 0.10 r₇ = 4.427 (Aspheric) d₇ = 0.99 n_(d4)= 1.78800 ν_(d4) = 47.37 r₈ = −7.290 d₈ = 1.20 n_(d5) = 1.84666 ν_(d5) =23.78 r₉ = 3.680 (Aspheric) d₉ = (Variable) r₁₀ = −7.523 d₁₀ = 1.20n_(d6) = 1.80610 ν_(d6) = 40.92 r₁₁ = −2.849 d₁₁ = 0.16 r₁₂ = −2.632 d₁₂= 1.16 n_(d7) = 1.49700 ν_(d7) = 81.54 r₁₃ = −6.396 (Aspheric) d₁₃ =0.79 r₁₄ = ∞ d₁₄ = 0.50 n_(d8) = 1.51633 ν_(d8) = 64.14 r₁₅ = ∞ d₁₅Aspherical Coefficients 4th surface K = 0.396 A₄ = 2.09373 × 10⁻³ A₆ =−1.62524 × 10⁻⁴ A₈ = 2.20952 × 10⁻⁴ A₁₀ = −2.31731 × 10⁻⁵ 7th surface K= −8.236 A₄ = 1.60630 × 10⁻³ A₆ = −3.38827 × 10⁻³ A₈ = −3.72604 × 10⁻⁴A₁₀ = 0 9th surface K = 0.344 A₄ = 8.07095 × 10⁻³ A₆ = −7.93864 × 10⁻⁴A₈ = 0 A₁₀ = 0 13th surface K = 0.000 A₄ = 3.88351 × 10⁻³ A₆ = −5.71375× 10⁻⁴ A₈ = 0 A₁₀ = 0 Zooming Data (∞) WE ST TE f (mm) 4.4 6.2 8.8F_(NO) 2.8 3.4 4.3 ω (°) 33.5 22.2 15.8 d₃ 2.76 1.21 0.10 d₉ 0.65 1.783.33

EXAMPLE 5-1

r₁ = −15.253 (Aspheric) d₁ = 0.60 n_(d1) = 1.69350 ν_(d1) = 53.21 r₂ =4.141 d₂ = 0.96 n_(d2) = 1.68893 ν_(d2) = 31.07 r₃ = 12.214 (Aspheric)d₃ = (Variable) r₄ = ∞ (Stop) d₄ = 0.10 r₅ = 9.919 (Aspheric) d₅ = 0.68n_(d3) = 1.49700 ν_(d3) = 81.54 r₆ = −11.002 d₆ = 0.10 r₇ = 3.141(Aspheric) d₇ = 1.33 n_(d4) = 1.74320 ν_(d4) = 49.34 r₈ = −6.830 d₈ =0.62 n_(d5) = 1.68893 ν_(d5) = 31.07 r₉ = 3.671 (Aspheric) d₉ =(Variable) r₁₀ = 11.080 d₁₀ = 1.06 n_(d6) = 1.68893 ν_(d6) = 31.07 r₁₁ =3.943 (Aspheric) d₁₁ = (Variable) r₁₂ = −13.947 d₁₂ = 1.11 n_(d7) =1.68893 ν_(d7) = 31.07 r₁₃ = −4.584 (Aspheric) d₁₃ = 1.69 r₁₄ = ∞ d₁₄ =0.50 n_(d8) = 1.51633 ν_(d8) = 64.14 r₁₅ = ∞ Aspherical Coefficients 1stsurface K = 19.399 A₄ = −9.52491 × 10⁻⁴ A₆ = 4.99000 × 10⁻⁵ A₈ = 1.01862× 10⁻⁵ A₁₀ = 0 3rd surface K = −14.812 A₄ = −8.97149 × 10⁻⁴ A₆ = 4.01691× 10⁻⁶ A₈ = 1.68687 × 10⁻⁵ A₁₀ = 0 5th surface K = 19.348 A₄ = −4.82828× 10⁻³ A₆ = 8.06209 × 10⁻⁴ A₈ = −1.99532 × 10⁻⁴ A₁₀ = 0 7th surface K =−1.011 A₄ = 7.47480 × 10⁻³ A₆ = −2.60867 × 10⁻⁴ A₈ = 8.69323 × 10⁻⁵ A₁₀= 0 9th surface K = −9.730 A₄ = 3.91180 × 10⁻² A₆ = −4.30584 × 10⁻³ A₈ =1.54137 × 10⁻³ A₁₀ = 0 11th surface K = −5.280 A₄ = 1.20789 × 10⁻² A₆ =−8.05017 × 10⁻⁴ A₈ = 1.88007 × 10⁻⁶ A₁₀ = 0 13th surface K = −1.512 A₄ =1.20543 × 10⁻⁴ A₆ = −1.73187 × 10⁻⁴ A₈ = 5.42052 × 10⁻⁶ A₁₀ = 0 ZoomingData (∞) WE ST TE f (mm) 4.7 7.6 13.0 F_(NO) 2.8 3.8 5.1 ω (°) 30.3 18.110.7 d₃ 5.47 2.88 0.18 d₉ 0.74 0.35 1.39 d₁₁ 0.74 3.72 5.38

EXAMPLE 5-2

r₁ = −8.395 (Aspheric) d₁ = 0.60 n_(d1) = 1.67790 ν_(d1) = 55.34 r₂ =4.439 d₂ = 0.98 n_(d2) = 1.68893 ν_(d2) = 31.07 r₃ = 21.458 (Aspheric)d₃ = (Variable) r₄ = ∞ (Stop) d₄ = 0.08 r₅ = 13.194 (Aspheric) d₅ = 0.65n_(d3) = 1.49700 ν_(d3) = 81.54 r₆ = −10.912 d₆ = 0.19 r₇ = 2.999(Aspheric) d₇ = 1.34 n_(d4) = 1.74320 ν_(d4) = 49.34 r₈ = −5.935 d₈ =0.60 n_(d5) = 1.68893 ν_(d5) = 31.07 r₉ = 3.541 (Aspheric) d₉ =(Variable) r₁₀ = −54.527 d₁₀ = 0.60 n_(d6) = 1.68893 ν_(d6) = 31.07 r₁₁= 6.260 (Aspheric) d₁₁ = (Variable) r₁₂ = 30.988 d₁₂ = 1.48 n_(d7) =1.68893 ν_(d7) = 31.07 r₁₃ = −5.446 (Aspheric) d₁₃ = 1.00 r₁₄ = ∞ d₁₄ =0.50 n_(d8) = 1.51633 ν_(d8) = 64.14 r₁₅ = ∞ Aspherical Coefficients 1stsurface K = 0.576 A₄ = −6.63222 × 10⁻⁴ A₆ = 5.19142 × 10⁻⁵ A₈ = 3.41858× 10⁻⁶ A₁₀ = 0 3rd surface K = −31.443 A₄ = −4.24448 × 10⁻⁴ A₆ =−2.32455 × 10⁻⁷ A₈ = 1.82275 × 10⁻⁵ A₁₀ = 0 5th surface K = 32.850 A₄ =−2.19377 × 10⁻³ A₆ = −7.72833 × 10⁻⁵ A₈ = 7.53132 × 10⁻⁶ A₁₀ = 0 7thsurface K = −1.055 A₄ = 7.33888 × 10⁻³ A₆ = 4.41996 × 10⁻⁴ A₈ = −1.81717× 10⁻⁵ A₁₀ = 0 9th surface K = −10.179 A₄ = 4.50999 × 10⁻² A₆ = −4.61578× 10⁻³ A₈ = 1.84744 × 10⁻³ A₁₀ = 0 11th surface K = −24.461 A₄ = 1.24411× 10⁻² A₆ = −2.06313 × 10⁻³ A₈ = 1.94143 × 10⁻⁴ A₁₀ = 0 13th surface K =−11.947 A₄ = −4.12632 × 10⁻³ A₆ = 2.43311 × 10⁻⁴ A₈ = −7.32948 × 10⁻⁶A₁₀ = 0 Zooming Data (∞) WE ST TE f (mm) 4.7 7.6 13.0 F_(NO) 2.8 3.8 5.0ω (°) 31.6 18.2 10.6 d₃ 6.04 3.32 0.55 d₉ 1.34 1.32 2.66 d₁₁ 1.76 4.495.93

EXAMPLE 6-1

r₁ = −235.855 d₁ = 0.60 n_(d1) = 1.69350 ν_(d1) = 53.21 r₂ = 3.549(Aspheric) d₂ = 1.59 r₃ = 6.625 d₃ = 0.91 n_(d2) = 1.84666 ν_(d2) =23.78 r₄ = 12.436 d₄ = (Variable) r₅ = ∞ (Stop) d₅ = 0.10 r₆ = 3.797(Aspheric) d₆ = 1.06 n_(d3) = 1.69350 ν_(d3) = 53.21 r₇ = −17.794 d₇ =0.10 r₈ = 7.931 (Aspheric) d₈ = 0.78 n_(d4) = 1.78800 ν_(d4) = 47.37 r₉= −4.713 d₉ = 0.60 n_(d5) = 1.68893 ν_(d5) = 31.07 r₁₀ = 2.574 d₁₀ =(Variable) r₁₁ = 4.259 d₁₁ = 0.66 n_(d6) = 1.49700 ν_(d6) = 81.54 r₁₂ =6.233 (Aspheric) d₁₂ = (Variable) r₁₃ = ∞ d₁₃ = 0.79 n_(d7) = 1.74320ν_(d7) = 49.34 r₁₄ = −8.029 d₁₄ = (Variable) (Aspheric) r₁₅ = ∞ d₁₅ =0.50 n_(d8) = 1.51633 ν_(d8) = 64.14 r₁₆ = ∞ Aspherical Coefficients 2ndsurface K = −0.565 A₄ = −1.29926 × 10⁻⁴ A₆ = 1.05590 × 10⁻⁴ A₈ =−7.93901 × 10⁻⁶ A₁₀ = 2.72375 × 10⁻⁷ 6th surface K = −0.137 A₄ =−1.31726 × 10⁻³ A₆ = −1.41891 × 10⁻⁴ A₈ = 6.88204 × 10⁻⁵ A₁₀ = −1.74013× 10⁻⁵ 8th surface K = −1.367 A₄ = −1.60327 × 10⁻³ A₆ = −1.35433 × 10⁻⁴A₈ = 0 A₁₀ = 0 12th surface K = 0.000 A₄ = 1.72530 × 10⁻³ A₆ = 2.23148 ×10⁻⁵ A₈ = 0 A₁₀ = 0 14th surface K = −14.842 A₄ = −1.74997 × 10⁻⁴ A₆ =2.64295 × 10⁻⁶ A₈ = 0 A₁₀ = 0 Zooming Data (∞) WE ST TE f (mm) 3.0 5.29.0 F_(NO) 2.8 3.7 5.3 ω (°) 45.5 25.7 15.3 d₄ 7.91 3.24 0.91 d₁₀ 0.242.88 6.07 d₁₂ 2.12 2.25 4.11 d₁₄ 1.01 1.07 0.18

EXAMPLE 6-2

r₁ = ∞ d₁ = 0.60 n_(d1) = 1.51633 ν_(d1) = 64.14 r₂ = 2.950 (Aspheric)d₂ = 2.52 r₃ = 5.433 d₃ = 0.80 n_(d2) = 1.84666 ν_(d2) = 23.78 r₄ =6.933 d₄ = (Variable) r₅ = ∞ (Stop) d₅ = 0.10 r₆ = 3.215 (Aspheric) d₆ =0.81 n_(d3) = 1.58313 ν_(d3) = 59.38 r₇ = −88.640 d₇ = 0.10 r₈ = 5.867(Aspheric) d₈ = 0.74 n_(d4) = 1.78800 ν_(d4) = 47.37 r₉ = −8.024 d₉ =0.60 n_(d5) = 1.68893 ν_(d5) = 31.07 r₁₀ = 2.566 d₁₀ = (Variable) r₁₁ =7.991 d₁₁ = 0.60 n_(d6) = 1.49700 ν_(d6) = 81.54 r₁₂ = 27.210 d₁₂ =(Variable) (Aspheric) r₁₃ = −29.417 d₁₃ = 0.99 n_(d7) = 1.49700 ν_(d7) =81.54 r₁₄ = −5.069 d₁₄ = (Variable) (Aspheric) r₁₅ = ∞ d₁₅ = 0.50 n_(d8)= 1.51633 ν_(d8) = 64.14 r₁₆ = ∞ Aspherical Coefficients 2nd surface K =−0.893 A₄ = 1.45261 × 10⁻³ A₆ = 1.41038 × 10⁻⁴ A₈ = −7.01509 × 10⁻⁶ A₁₀= 4.11221 × 10⁻⁷ 6th surface K = 0.128 A₄ = 1.53677 × 10⁻⁵ A₆ = −8.68099× 10⁻⁵ A₈ = 2.50336 × 10⁻⁴ A₁₀ = −3.99233 × 10⁻⁵ 8th surface K = −2.777A₄ = −2.28635 × 10⁻³ A₆ = −5.33394 × 10⁻⁴ A₈ = −1.51884 × 10⁻⁴ A₁₀ = 012th surface K = 0.000 A₄ = 2.30056 × 10⁻³ A₆ = −1.45665 × 10⁻⁴ A₈ =2.87717 × 10⁻⁵ A₁₀ = 0 14th surface K = −2.859 A₄ = −1.27245 × 10⁻⁴ A₆ =−4.60322 × 10⁻⁵ A₈ = −3.26441 × 10⁻⁶ A₁₀ = 0 Zooming Data (∞) WE ST TE f(mm) 3.0 5.2 9.0 F_(NO) 2.8 3.3 5.4 ω (°) 43.9 25.8 15.8 d₄ 7.57 1.590.74 d₁₀ 0.37 0.66 3.80 d₁₂ 1.44 1.79 6.68 d₁₄ 1.96 3.15 0.10

EXAMPLE 6-3

r₁ = −39.641 d₁ = 0.60 n_(d1) = 1.69350 ν_(d1) = 53.21 r₂ = 3.758(Aspheric) d₂ = 1.62 r₃ = 7.085 d₃ = 0.83 n_(d2) = 1.84666 ν_(d2) =23.78 r₄ = 13.743 d₄ = (Variable) r₅ = ∞ (Stop) d₅ = 0.10 r₆ = 3.644(Aspheric) d₆ = 1.36 n_(d3) = 1.69350 ν_(d3) = 53.21 r₇ = −23.518 d₇ =0.10 r₈ = 8.588 (Aspheric) d₈ = 0.82 n_(d4) = 1.78800 ν_(d4) = 47.37 r₉= −3.659 d₉ = 0.60 n_(d5) = 1.68893 ν_(d5) = 31.07 r₁₀ = 2.800 d₁₀ =(Variable) r₁₁ = 4.441 d₁₁ = 1.29 n_(d6) = 1.49700 ν_(d6) = 81.54 r₁₂ =4.321 (Aspheric) d₁₂ = (Variable) r₁₃ = 5.613 d₁₃ = 1.20 n_(d7) =1.69350 ν_(d7) = 53.21 r₁₄ = 556.044 d₁₄ = 0.22 (Aspheric) r₁₅ = ∞ d₁₅ =0.50 n_(d8) = 1.51633 ν_(d8) = 64.14 r₁₆ = ∞ Aspherical Coefficients 2ndsurface K = −0.730 A₄ = 1.40877 × 10⁻⁶ A₆ = 1.25212 × 10⁻⁴ A₈ = −9.63026× 10⁻⁶ A₁₀ = 3.57391 × 10⁻⁷ 6th surface K = 0.181 A₄ = −3.50134 × 10⁻⁴A₆ = −9.65305 × 10⁻⁵ A₈ = 1.52691 × 10⁻⁴ A₁₀ = −3.81912 × 10⁻⁵ 8thsurface K = −19.376 A₄ = −1.33804 × 10⁻³ A₆ = −1.00926 × 10⁻³ A₈ = 0 A₁₀= 0 12th surface K = 0.000 A₄ = −1.98092 × 10⁻⁴ A₆ = 1.58372 × 10⁻⁴ A₈ =0 A₁₀ = 0 14th surface K = 0.000 A₄ = 4.78191 × 10⁻³ A₆ = −3.69614 ×10⁻⁴ A₈ = 0 A₁₀ = 0 Zooming Data (∞) WE ST TE f (mm) 3.0 5.2 9.0 F_(NO)2.8 3.7 5.2 ω (°) 46.4 25.8 14.8 d₄ 7.08 2.79 0.22 d₁₀ 0.23 4.07 6.51d₁₂ 1.91 0.90 2.49

EXAMPLE 7-1

r₁ = 16.444 (Aspheric) d₁ = 1.11 n_(d1) = 1.49700 ν_(d1) = 81.54 r₂ =−10.268 d₂ = (Variable) r₃ = −6.588 (Aspheric) d₃ = 0.60 n_(d2) =1.81600 ν_(d2) = 46.62 r₄ = 4.660 d₄ = 0.81 n_(d3) = 1.84666 ν_(d3) =23.78 r₅ = 10.739 d₅ = (Variable) r₆ = ∞ (Stop) d₆ = (Variable) r₇ =2.889 (Aspheric) d₇ = 1.73 n_(d4) = 1.72916 ν_(d4) = 54.68 r₈ = −6.939d₈ = 0.10 r₉ = −296.907 d₉ = 1.00 n_(d5) = 1.84666 ν_(d5) = 23.78 r₁₀ =2.764 (Aspheric) d₁₀ = (Variable) r₁₁ = 10.958 d₁₁ = 0.69 n_(d6) =1.84666 ν_(d6) = 23.78 (Aspheric) r₁₂ = −38.512 d₁₂ = (Variable) r₁₃ = ∞d₁₃ = 0.50 n_(d7) = 1.51633 ν_(d7) = 64.14 r₁₄ = ∞ AsphericalCoefficients 1st surface K = 0.000 A₄ = −3.90951 × 10⁻⁴ A₆ = −1.51396 ×10⁻⁵ A₈ = −1.67063 × 10⁻⁷ A₁₀ = 0 3rd surface K = −8.941 A₄ = −2.25798 ×10⁻³ A₆ = 1.84228 × 10⁻⁴ A₈ = −6.78364 × 10⁻⁶ A₁₀ = 0 7th surface K =0.149 A₄ = −5.76087 × 10⁻³ A₆ = −3.03438 × 10⁻⁴ A₈ = −1.86281 × 10⁻⁴ A₁₀= 1.78319 × 10⁻⁵ 10th surface K = −0.789 A₄ = 1.46423 × 10⁻² A₆ =1.70602 × 10⁻³ A₈ = −1.02432 × 10⁻⁴ A₁₀ = 0 11th surface K = −1.302 A₄ =1.42750 × 10⁻³ A₆ = 3.40229 × 10⁻⁵ A₈ = −3.10139 × 10⁻⁶ A₁₀ = 0 ZoomingData (∞) WE ST TE f (mm) 4.4 7.6 13.2 F_(NO) 2.8 3.3 4.3 ω (°) 33.4 17.910.5 d₂ 0.21 1.63 3.00 d₅ 4.45 1.68 0.16 d₆ 1.86 1.55 0.10 d₁₀ 0.36 1.532.25 d₁₂ 3.24 3.73 4.61

EXAMPLE 7-2

r₁ = 12.875 (Aspheric) d₁ = 1.22 n_(d1) = 1.49700 ν_(d1) = 81.54 r₂ =−11.898 d₂ = (Variable) r₃ = −6.694 (Aspheric) d₃ = 0.60 n_(d2) =1.81600 ν_(d2) = 46.62 r₄ = 4.386 d₄ = 0.38 r₅ = 5.629 d₅ = 0.78 n_(d3)= 1.84666 ν_(d3) = 23.78 r₆ = 15.581 d₆ = (Variable) r₇ = ∞ (Stop) d₇ =(Variable) r₈ = 2.890 (Aspheric) d₈ = 2.00 n_(d4) = 1.72916 ν_(d4) =54.68 r₉ = −7.475 d₉ = 0.10 r₁₀ = −40.151 d₁₀ = 0.60 n_(d5) = 1.84666ν_(d5) = 23.78 r₁₁ = 3.043 (Aspheric) d₁₁ = (Variable) r₁₂ = 8.251(Aspheric) d₁₂ = 0.65 n_(d6) = 1.84666 ν_(d6) = 23.78 r₁₃ = 110.712 d₁₃= (Variable) r₁₄ = ∞ d₁₄ = 0.50 n_(d7) = 1.51633 ν_(d7) = 64.14 r₁₅ = ∞Aspherical Coefficients 1st surface K = 0.000 A₄ = −2.87331 × 10⁻⁴ A₆ =−1.36425 × 10⁻⁵ A₈ = −2.10759 × 10⁻⁷ A₁₀ = 0 3rd surface K = −6.859 A₄ =−6.46103 × 10⁻⁴ A₆ = 6.43816 × 10⁻⁵ A₈ = −2.35771 × 10⁻⁶ A₁₀ = 0 8thsurface K = 0.202 A₄ = −4.23004 × 10⁻³ A₆ = −5.62239 × 10⁻⁴ A₈ = 1.16888× 10⁻⁵ A₁₀ = −2.46485 × 10⁻⁵ 11th surface K = −0.930 A₄ = 1.38536 × 10⁻²A₆ = 1.65230 × 10⁻³ A₈ = 1.48060 × 10⁻⁴ A₁₀ = 0 12th surface K = −4.825A₄ = 1.27515 × 10⁻³ A₆ = 1.23670 × 10⁻⁴ A₈ = −2.14636 × 10⁻⁵ A₁₀ = 0Zooming Data (∞) WE ST TE f (mm) 4.4 7.6 13.2 F_(NO) 2.8 3.5 4.1 ω (°)33.0 17.9 10.5 d₂ 0.25 1.67 2.81 d₆ 5.38 3.17 0.15 d₇ 1.16 0.15 0.10 d₁₁0.30 1.42 2.02 d₁₃ 3.87 4.53 5.87

EXAMPLE 7-3

r₁ = 11.725 (Aspheric) d₁ = 1.09 n_(d1) = 1.49700 ν_(d1) = 81.54 r₂ =−16.531 d₂ = (Variable) r₃ = −8.820 (Aspheric) d₃ = 0.60 n_(d2) =1.81600 ν_(d2) = 46.62 r₄ = 4.699 d₄ = 0.42 r₅ = 5.723 d₅ = 0.74 n_(d3)= 1.84666 ν_(d3) = 23.78 r₆ = 13.620 d₆ = (Variable) r₇ = ∞ (Stop) d₇ =(Variable) r₈ = 3.020 (Aspheric) d₈ = 1.71 n_(d4) = 1.72916 ν_(d4) =54.68 r₉ = −7.650 d₉ = 0.10 r₁₀ = −55.896 d₁₀ = 0.89 n_(d5) = 1.84666ν_(d5) = 23.78 r₁₁ = 3.002 (Aspheric) d₁₁ = (Variable) r₁₂ = 5.067(Aspheric) d₁₂ = 0.80 n_(d6) = 1.84666 ν_(d6) = 23.78 r₁₃ = 12.083 d₁₃ =(Variable) r₁₄ = ∞ d₁₄ = 0.50 n_(d7) = 1.51633 ν_(d7) = 64.14 r₁₅ = ∞Aspherical Coefficients 1st surface K = 0.000 A₄ = −1.66609 × 10⁻⁴ A₆ =−2.74210 × 10⁻⁶ A₈ = −1.85730 × 10⁻⁷ A₁₀ = 0 3rd surface K = −12.939 A₄= −1.39316 × 10⁻³ A₆ = 9.75592 × 10⁻⁵ A₈ = −2.56373 × 10⁻⁶ A₁₀ = 0 8thsurface K = −0.005 A₄ = −3.06313 × 10⁻³ A₆ = −2.32293 × 10⁻⁴ A₈ =−7.53412 × 10⁻⁵ A₁₀ = 3.30742 × 10⁻⁶ 11th surface K = −1.189 A₄ =1.28018 × 10⁻² A₆ = 1.75616 × 10⁻³ A₈ = −7.21525 × 10⁻⁵ A₁₀ = 0 12thsurface K = −4.764 A₄ = 3.80909 × 10⁻³ A₆ = −1.52897 × 10⁻⁴ A₈ = 5.78542× 10⁻⁶ A₁₀ = 0 Zooming Data (∞) WE ST TE f (mm) 4.4 7.6 13.2 F_(NO) 2.83.4 3.9 ω (°) 34.3 17.9 10.4 d₂ 0.24 2.31 4.55 d₆ 4.46 2.39 0.15 d₇ 2.611.19 0.10 d₁₁ 0.25 1.54 3.28 d₁₃ 3.31 3.45 2.80

Set out below are the values of conditions (2A) and (3A) in Examples 1-1and 1-2.

Example 1-1 Example 1-2 Condition (2A) 2.85 5.36 Condition (3A)(Object-Side Lens) 1.16 0.68 (Image-Side Lens) 1.03 —

Set out below are the values of conditions (2B) and (3B) in Examples 2-1and 2-2.

Example 2-1 Example 2-2 Condition (2B) 2.85 5.36 Condition (3B)(Object-Side Lens) 1.16 0.68 (Image-Side Lens) 1.03 —

Set out below are the values of conditions (2C), (3C) and (4C) inExamples 3-1 and 3-2.

Example 3-1 Example 3-2 Condition (2C) 6.08 3.95 Condition (3C)(Object-Side Lens) 1.43 1.13 (Image-Side Lens) 1.89 0.78 Condition (4C)12.05 4.34

Set out below are the values of conditions (2C), (3C) and (4C) inExamples 3-1 and 3-2.

Example 3-1 Example 3-2 Condition (2C) 6.08 3.95 Condition (3C)(Object-Side Lens) 1.43 1.13 (Image-Side Lens) 1.89 0.78 Condition (4C)12.05 4.34

Set out below are the values of conditions (2D), (3D) and (4D) inExamples 4-1 and 4-2.

Example 4-1 Example 4-2 Condition (2C) 4.17 2.38 Condition (3D)(Object-Side Lens) 2.32 2.11 (Image-Side Lens) 1.17 1.50 Condition (4D)3.50 3.07

Set out below are the values of conditions (2E), (3E) and (5E) inExamples 5-1 and 5-2.

Example 5-1 Example 5-2 Condition (2E) 3.63 3.26 Condition (3E)(Object-Side Lens) 2.36 2.55 (Image-Side Lens) 1.60 1.48 Condition (5E)4.56 4.01

Set out below are the values of conditions (2F), (3F), (4F) and 5(F) inExamples 6-1, 6-2 and 6-3.

Ex. 6-1 Ex. 6-2 Ex. 6-3 Condition (2F) 6.98 10.65 6.57 Condition (3F)(Object-Side Lens) 1.94 1.59 2.50 (Image-Side Lens) 1.28 1.39 1.17Condition (4F) 6.40 4.58 202.83 Condition (5F) 3.62 4.10 4.03

Set out below are the values of conditions (2G), (3G), (4G) and 5(G) inExamples 7-1, 7-2 and 7-3.

Ex. 7-1 Ex. 7-2 Ex. 7-3 Condition (2G) 4.59 4.96 4.92 Condition (3G)3.62 3.72 3.97 Condition (4G) 1.96 2.30 2.06 Condition (5G) 3.15 3.123.81

By the way, although glass is used for all the lenses in the zoomoptical systems according to the above example, it is acceptable to usea plastic material for them. With the use of resinous materials forlenses, it is possible to easily mass-fabricate them by moldingprocesses for the resinous materials. Expensive resinous materials makeit possible to achieve expensive optical systems.

It is also acceptable to use organic-inorganic composite materials inplace of glass. Organic-inorganic composite materials usable herein arenow explained.

In an organic-inorganic composite material, an organic component and aninorganic component are mixed together into a composite material at amolecular level or a nano-scale. Some available forms include (1) astructure wherein a polymeric matrix comprising an organic skeleton anda matrix comprising an inorganic skeleton are entangled together andpenetrated into each other, (2) a structure wherein inorganic fineparticles (so-called nano-particles) much smaller than the wavelength oflight on a nano-scale are uniformly dispersed throughout a polymericmatrix comprising an organic skeleton, and (3) a combined structure ofboth.

Between the organic component and the inorganic component there are someinteractions such as intermolecular forces, e.g., hydrogen bonds,dispersion forces and Coulomb force, attractive forces resulting fromcovalent bonds, ionic bonds and interaction of π electron clouds, etc.In the organic-inorganic composite material, the organic component andthe inorganic component are mixed together at a molecular level or at ascale level smaller than the wavelength of light. For this reason, thatcomposite material provides a transparent material because of havinglittle or no influence on light scattering. As can also be derived fromMaxwell equation, the composite material possesses the opticalcharacteristics of each of the organic and inorganic components.Therefore, the organic-inorganic composite material can have variousoptical properties (such as refractive index and chromatic dispersion)depending on the type and quantitative ratio of the organic andinorganic components present. Thus, it is possible to obtain variousoptical properties by blending together the organic and inorganiccomponents at any desired ratio.

Some exemplary compositions of an organic-inorganic composite materialcomprising an acrylate resin (of the ultraviolet curable type) andnano-particles of zirconia (ZrO₂) are shown in Table 1; some exemplarycompositions of an organic-inorganic composite material comprising anacrylate resin and nano-particles of zirconia(ZrO₂)/alumina (Al₂O₃) inTable 2; some exemplary compositions of an organic-inorganic compositematerial comprising an acrylate resin and nano-particles of niobiumoxide (Nb₂O₅) in Table 3; and some exemplary compositions of an acrylateresin and nano-particles of zirconium alkoxide/alumina (Al₂O₃) in Table4.

TABLE 1 Zirconia Content n_(d) ν_(d) n_(C) n_(F) n_(g) 0 (100% 1.4923657.85664 1.48981 1.49832 1.50309 acrylic) 0.1 1.579526 54.85037 1.575791.586355 1.59311 0.2 1.662128 53.223 1.657315 1.669756 1.678308 0.31.740814 52.27971 1.735014 1.749184 1.759385 0.4 1.816094 51.717261.809379 1.825159 1.836887 0.5 1.888376 51.3837 1.880807 1.8980961.911249

TABLE 2 Al₂O₃* ZrO₂* n_(d) ν_(d) n_(C) n_(F) n_(g) Remarks 0.1 0.41.831515 53.56672 1.824581 1.840374 1.8151956 50% acrylate 0.2 0.31.772832 56.58516 1.767125 1.780783 1.790701 0.3 0.2 1.712138 60.976871.707449 1.719127 1.727275 0.4 0.1 1.649213 67.85669 1.645609 1.6551771.661429 0.2 0.2 1.695632 58.32581 1.690903 1.702829 1.774891 Al₂O₃*:quantitative ratio of Al₂O₃ ZrO₂*: quantitative ratio of ZrO₂

TABLE 3 Nb₂O₅* Al₂O₃* n_(d) ν_(d) n_(C) n_(F) n_(g) 0.1 0 1.58986129.55772 1.584508 1.604464 1.617565 0.2 0 1.681719 22.6091 1.6738571.70401 1.724457 0.3 0 1.768813 19.52321 1.758673 1.798053 1.8251 0.4 01.851815 17.80818 1.839538 1.887415 1.920475 0.5 0 1.931253 16.732911.91708 1.972734 2.011334 Nb₂O₅*: content of Nb₂O₅ Al₂O₃*: content ofAl₂O₃

TABLE 4 Al₂O₃* ZA* n_(d) ν_(d) n_(C) n_(F) 0 0.2 1.533113 58.398371.530205 1.539334 0.1 0.27 1.54737 62.10192 1.544525 1.553339 0.2 0.241.561498 66.01481 1.558713 1.567219 0.3 0.21 1.575498 70.15415 1.5727741.580977 0.4 0.18 1.589376 74.53905 1.586709 1.159616 Al₂O₃*: content ofAl₂O₃ (film) ZA*: zirconia alkoxide

Electronic systems comprising such zoom or image-formation opticalsystems as described above are now explained. Used for such electronicsystems is a taking unit wherein an object image formed through theabove zoom optical system is received by an image pickup device such asCCD for taking. The electronic systems, for instance, include digitalcameras, video cameras, digital video units, information processors suchas personal computers and mobile computers, telephone sets in generaland easy-to-carry cellular phones in particular and personal digitalassistants, as set forth below.

FIGS. 57, 58 and 59 are conceptual illustrations of a digital camera, inwhich the zoom optical system of the invention is incorporated as ataking optical system 41. FIG. 573 is a front perspective view of theappearance of a digital camera 40, and FIG. 58 is a rear perspectiveview of the same. FIG. 59 is a sectional view of the construction of thedigital camera 40.

In this embodiment, the digital camera 40 comprises a taking opticalsystem 41, a finder optical system 43, a shutter 45, a flash 46, aliquid crystal monitor 47 and so on. The taking optical system 41 islocated on a taking optical path 42, the finder optical system 43 isplaced on a finder optical path 44 separate from the taking optical path42, and the shutter 45 is disposed on an upper portion of the camera 40.As the user presses down the shutter 45, it causes taking to occurthrough a taking optical system 41, for instance, the zoom opticalsystem of Example 1-1 of the first zoom optical system.

An object image formed by the taking optical system 41 is formed on theimage pickup plane of a CCD 49 via a plane-parallel plate and a coverglass. The plane-parallel plate is provided with an ultraviolet cutcoating. The plane-parallel plate could also have a low-pass filterfunction. The object image received at CCD 49 is shown as an electronicimage on the liquid crystal monitor 47 via processing means 51, whichmonitor is mounted on the back of the camera. This processing means 51could be connected with recording means 52 to record therein takenelectronic images.

It is noted that the recording means 52 could be provided separatelyfrom the processing means 51 or, alternatively, it could be a floppydisk, a memory card, an MO or the like. Otherwise, the recording means52 could be constructed in such a way as to implement electronicrecording or writing. This camera could also be constructed in the formof a silver-halide camera using a silver-halide film in place of CCD 49.

Moreover, a finder objective optical system 53 is located on the finderoptical path 44. An object image formed by that finder objective opticalsystem 53 is formed on a field frame 57, which is attached to a Porroprism 55 that is an image-erecting member. In the rear of the Porroprism 55 there is located an eyepiece optical system 59 for guiding anerected image into the eyeball E of a viewer. Three cover members 50 areprovided: two on the entrance sides of the taking optical system 41 andthe finder objective optical system 53 and one on the exit side of theeyepiece optical system 59. While plane-parallel plates are herein usedfor the cover members 50, it is noted that lenses having power couldalso be used.

The thus constructed digital camera 40 is improved in terms ofperformance and size reductions, because the taking optical system 41has high performance and is slimmed down.

FIGS. 60, 61 and 62 are illustrative of a personal computer that is oneexample of the information processor in which the zoom optical system ofthe invention is used as an objective optical system. FIG. 60 is a frontperspective view of a personal computer 300 in use with a cover put up,FIG. 61 is a side view of a taking optical system 303 in the personalcomputer 300, and FIG. 62 is a side view of the state of FIG. 60.

The personal computer 300 comprises a keyboard 301 that enables theoperator to enter information from outside, a monitor 302 for presentinginformation to the operator and a taking optical system 303 for takingimages of the operator himself or herself and surrounding images. Inaddition, the personal computer 300 comprises information processingmeans, recording means, etc., although not shown.

Here the keyboard 301 is provided for the operator to enter informationfrom the outside in the computer. The information processing means andrecording means are not shown. The monitor 302 could be any one of atransmission type liquid crystal display device illuminated from itsback surface by a backlight (not shown), a reflection type liquidcrystal display device designed to display images by reflection of lightcoming from the front, a CRT display or the like. The taking opticalsystem 303 is provided for taking an image of the operator andsurrounding images. While the taking optical system 303 is shown asbeing built in the right-upper portion of the monitor 302, it isunderstood that it is not limited thereto; it could be located somewherearound the monitor 302 or keyboard 301.

This taking optical system 303 comprises, on a taking optical path 304,an objective lens 112 comprising the (roughly sketched) zoom opticalsystem of the invention and an image pickup device chip 162 forreceiving an image. These are built in the personal computer 300.

Here, a plane-parallel plate group F such as an optical low-pass filteris additionally applied onto the image pickup device chip 162. That is,the image pickup device chip 162 and the plane-parallel plate group Fare set up as an image pickup unit 160 that can be fitted into the rearend of the lens barrel 113 of the objective lens 112 in one-touchoperation, so that alignment of the objective lens 112 with the imagepickup device chip 162, and surface-to-surface space adjustment aredispensed with, leading to easy assembling. At the front end of the lensbarrel 113, there is located a cover glass 114 for protection of theobjective lens 112. It is here noted that the driving mechanisms for thezoom optical system in the lens barrel 113 is not shown.

An object image received at the image pickup device chip 162 is enteredvia a terminal 166 in the processing means of the personal computer 300,and shown as an electronic image on the monitor 302. As an example, animage 305 taken of the operator is shown in FIG. 60. This image 305could be transmitted to and shown on a personal computer on the otherend via suitable processing means and the Internet or telephone line.

FIGS. 63( a), 63(b) and 63(c) are illustrative in conception of atelephone set that is another example of the information processor inwhich the zoom optical system of the invention is built, especially aconvenient-to-carry cellular phone. FIG. 63( a) and FIG. 63( b) are afront view and a side view of a cellular phone 400, respectively, andFIG. 63( c) is a sectional view of a taking optical system 405.

The cellular phone 400 comprises a microphone 401, a speaker 402, aninput dial 403, a monitor 404, a taking optical system 405, an antenna406, and processing means (not shown). Here the microphone 401 is toenter the voice of the operator as information in the cellular phone,and the speaker 402 is to produce the voice of the person on the otherend. The input dial 403 includes a button by which the operator entersinformation in the cellular phone. The monitor 404 is to show the imagestaken of the operator per se or the person on the other end and indicateinformation such as a telephone number. A liquid crystal display is usedas the monitor 404. The antenna 406 is to transmit and receivecommunications waves. It is here noted that the components or theirpositions are not limited to those shown.

The taking optical system 405 is located on a taking optical path 407.That taking optical system 405 comprises an objective lens 112comprising the (roughly sketched) zoom optical system of the inventionand an image pickup device chip 162 for receiving an object image. Theseare built in the cellular phone 400.

Here, a plane-parallel plate group F such as an optical low-pass filteris additionally applied onto the image pickup device chip 162. That is,the image pickup device chip 162 and the plane-parallel plate group Fare set up as an image pickup unit 160 that can be fitted into the rearend of the lens barrel 113 of the objective lens 112 in one-touchoperation, so that alignment of the objective lens 112 with the imagepickup device chip 162, and surface-to-surface space adjustment aredispensed with, leading to easy assembling. At the front end of the lensbarrel 113, there is located a cover glass 114 for protection of theobjective lens 112. It is noted that the driving mechanism for the zoomoptical system in the lens barrel 113 is not shown.

An object image received at the image pickup device chip 162 is enteredvia a terminal 166 in processing means (not shown), so that the objectimage can be displayed as an electronic image on the monitor 404. Theprocessing means also includes a signal processing function forconverting information about the object image received at the imagepickup device chip 162 into transmittable signals, thereby sending theimage to the person on the other end, so that the object image can bedisplayed on a monitor on the other end.

POSSIBLE INDUSTRIAL APPLICATIONS

With the invention, an effective tradeoff can be offered between thecost reductions and the size reductions of a zoom optical system, and anelectronic system relying on it, too, can be slimmed down at low costs.

1. A zoom optical system comprising, in order from an object sidethereof, a first lens group having positive refracting power, a secondlens group having negative refracting power, a third lens group havingpositive refracting power and a fourth lens group having positiverefracting power, wherein: at least one lens is formed by molding of afirst lens blank that provides a surface including at least an opticalfunction surface after molding, and a second lens blank that provides asurface other than said surface including at least an optical functionsurface after molding, and comprises a one-piece lens wherein said firstlens blank and said second blank are integrated together, said secondlens group or said fourth lens group comprises at least one saidone-piece lens, and at least one positive lens is positioned in saidsecond lens group, and satisfies the following condition:0.1<HH2/φ2<15  (3G) where HH2 is a principal point spacing (mm) of thepositive lens in the second lens group and φ2 is a refracting power ofthe positive lens in the second lens group.
 2. A zoom optical systemcomprising, in order from an object side thereof, a first lens grouphaving positive refracting power, a second lens group having negativerefracting power, a third lens group having positive refracting powerand a fourth lens group having positive refracting power, wherein atleast one lens is formed by molding of a first lens blank that providesa surface including at least an optical function surface after molding,and a second lens blank that provides a surface other than said surfaceincluding at least an optical function surface after molding, whereinthe first lens blank and the second lens blank are integrated into a onepiece lens, and at least one positive lens is positioned in said firstlens group and satisfies the following condition:0.1<HH1/φ1<20  (2G) where HH1 is a principal point spacing (mm) of thepositive lens in the first lens group and φ1 is a refracting power ofthe positive lens in the first lens group.
 3. A zoom optical systemcomprising, in order from an object side thereof, a first lens grouphaving positive refracting power, a second lens group having negativerefracting power, a third lens group having positive refracting powerand a fourth lens group having positive refracting power, wherein atleast one lens is formed by molding of a first lens blank that providesa surface including at least an optical function surface after molding,and a second lens blank that provides a surface other than said surfaceincluding at least an optical function surface after molding, whereinthe first lens blank and the second lens blank are integrated into aone-piece lens, and at least one positive lens is positioned in saidthird lens group and satisfies the following condition:0.1<HH3/φ3<8  (4G) where HH3 is a principal point spacing (mm) of thepositive lens in the third lens group and φ3 is a refracting power ofthe positive lens in the third lens group.
 4. A zoom optical systemcomprising, in order from an object side thereof, a first lens grouphaving positive refracting power, a second lens group having negativerefracting power, a third lens group having positive refracting powerand a fourth lens group having positive refracting power, wherein atleast one lens is formed by molding of a first lens blank that providesa surface including at least an optical function surface after molding,and a second lens blank that provides a surface other than said surfaceincluding at least an optical function surface after molding, whereinthe first lens blank and the second lens blank are integrated into aone-piece lens, and at least one positive lens is positioned in saidfourth lens group and satisfies the following condition:0.1<HH4/φ4<10  (5G) where HH4 is a principal point spacing (mm) of thepositive lens in the fourth lens group and φ4 is a refracting power ofthe positive lens in the fourth lens group.